Algebra for College Students (10th Edition)
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Quotient: ; Remainder: 16 ; Write the coefficients... more
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Quotient: ; Remainder: 10 ; Write the coefficients... more
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Quotient: ; Remainder: 0 ; Write the coefficients ... more
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The degree of the given polynomial is smaller than... more
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Polynomial long division is an algorithm for ... more
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The given divisor changes to in synthetic ... more
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The last term of the quotient line represents the ... more
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The quotient line of the form represents the ... more
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The quotient line of the form represents the ... more
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Quotient: ; Remainder: 0 ; Write the coefficients ... more
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Quotient: ; Remainder: 0 ; Write the coefficients ... more
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Quotient: ; Remainder: 0 ; Write the coefficients ... more
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Quotient: ; Remainder: 0 ; Write the coefficients ... more
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Quotient: ; Remainder: 1 ; Write the coefficients ... more
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Quotient: ; Remainder: ; Write the coefficients of... more
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Quotient: ; Remainder: ; Write the coefficients of... more
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Quotient: ; Remainder: 6 ; Write the coefficients ... more
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Quotient: ; Remainder: 0 ; Write the coefficients ... more
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Quotient: ; Remainder: 0 ; Write the coefficients ... more
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Quotient: ; Remainder: 0 ; Write the coefficients ... more
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Quotient: ; Remainder: 0 ; Write the coefficients ... more
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Quotient: ; Remainder: 0 ; Write the coefficients ... more
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Quotient: ; Remainder: 2 ; Write the coefficients ... more
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Quotient: ; Remainder: 8 ; Write the coefficients ... more
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Quotient: ; Remainder: ; The given dividend is a ... more
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Quotient: ; Remainder: 0 ; Rewrite the dividend as... more
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Quotient: ; Remainder: 0 ; The given dividend is a... more
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Quotient: ; Remainder: 4 ; The given dividend is a... more
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Quotient: ; Remainder: ; The given dividend is a ... more
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Quotient: ; Remainder: 15 ; The given dividend has... more
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Quotient: ; Remainder: ; The given dividend has a ... more
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Quotient: ; Remainder: 0 ; The given dividend is a... more
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Quotient: ; Remainder: 0 ; The given dividend is a... more
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Quotient: ; Remainder: 167 ; The given dividend ... more
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Quotient: ; Remainder: 12 ; The given dividend is ... more
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Quotient: ; Remainder: 0 ; The given dividend has... more
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Quotient: ; Remainder: 47 ; The given dividend ... more
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Quotient: ; Remainder: 0 ; The given dividend ... more
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Quotient: ; Remainder: 0 ; The given dividend ... more
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Quotient: ; Remainder: ; The given dividend does ... more
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Quotient: ; Remainder: 0 ; The given dividend ... more
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Quotient: ; Remainder: 0 ; The given dividend ... more
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Quotient: ; Remainder: 2 ; The given dividend ... more
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Quotient: ; Remainder: 0 ; The given dividend is ... more
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Quotient: ; Remainder: 0 ; The given dividend is ... more
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Quotient: ; Remainder: ; The given dividend is a ... more
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Quotient: ; Remainder: 2 ; The given dividend is ... more
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Quotient: ; Remainder: ; The given dividend is a ... more
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Quotient: ; Remainder: ; The given dividend is a ... more
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Quotient: ; Remainder: 0 ; The given dividend is ... more
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Quotient: ; Remainder: 0 ; The given dividend ... more
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Synthetic division provides a shortcut way to ... more
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It is restricted to use the synthetic division ... more
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0 ; The remainder theorem states that if the ... more
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The factor theorem states that the polynomial has ... more
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The factor theorem states that the polynomial has ... more
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; The factor theorem states that the polynomial ... more
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; The factor theorem states that the polynomial ... more
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Use the factor theorem and substitute 1 for in ... more
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The remainder theorem states that if the ... more
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The remainder theorem states that if the ... more
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The factor theorem states that the polynomial has ... more
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The factor theorem states that the polynomial has ... more
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The factor theorem states that the polynomial has ... more
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The factor theorem states that the polynomial has ... more
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; Substitute for into the given function and ... more
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; Substitute 2 for into the given function and ... more
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; Substitute 8 for into the given function and ... more
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; Substitute 7 for into the given function and ... more
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8751 ; Substitute 3 for into the given function ... more
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; Substitute for into the given function and ... more
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31 ; Substitute for into the given function and ... more
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; Substitute for into the given function and ... more
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; Substitute 4 for into the given function and ... more
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8494 ; Substitute 5 for into the given function ... more
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Yes ; The factor theorem states that is a factor ... more
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Yes ; The first given polynomial can be written as... more
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No ; The first given polynomial can be written as... more
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No ; The factor theorem states that is a factor ... more
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Yes ; The factor theorem states that is a factor ... more
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Yes ; The factor theorem states that is a factor ... more
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Yes ; The first given polynomial can be written as... more
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Yes ; The first given polynomial can be written as... more
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No ; The factor theorem states that is a factor ... more
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No ; The first given polynomial can be written as... more
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Yes ; The first given polynomial can be written as... more
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Yes ; The factor theorem states that is a factor ... more
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Yes ; The factor theorem states that is a factor ... more
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Yes ; The first given polynomial can be written as... more
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Divide the second given polynomial function by the... more
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Divide the second given polynomial function by ... more
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Divide the second given polynomial function by ... more
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Divide the second given polynomial function by the... more
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Divide the second given polynomial function by the... more
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Divide the second given polynomial function by the... more
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Divide the second given polynomial function by ... more
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Divide the polynomial function by the polynomial ... more
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Divide the second polynomial function by the ... more
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Divide the second polynomial function by the ... more
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1, ; The factor theorem states that for any ... more
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6 ; The factor theorem states that for any ... more
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6 ; The factor theorem states that for any ... more
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; The factor theorem states that for any ... more
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There does not exist any real number such that ... more
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For the given polynomial , . Therefore by factor ... more
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For the given polynomial , . Therefore by factor ... more
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For the given polynomial , . Therefore by factor ... more
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The remainder theorem helps to obtain the value of... more
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The factor theorem helps to factorize any ... more
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For the given polynomial , . Therefore by factor ... more
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For the given polynomial , . Therefore by factor ... more
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{, , } ; The rational root theorem states that for... more
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{, , 2} ; The rational root theorem states that ... more
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{, , } ; The rational root theorem states that for... more
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; The property of polynomials states that the ... more
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The property of polynomials states that the ... more
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The property of polynomials states that the ... more
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The rational root theorem states that for any ... more
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The rational root theorem states that for any ... more
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The rational root theorem states that for any ... more
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If a polynomial with real coefficients has non ... more
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This statement is true and can be proved by ... more
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This statement is true and can be proved by ... more
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{, 1, 4} ; The rational root theorem states that ... more
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{, , 2} ; The rational root theorem states that ... more
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; The rational root theorem states that for any ... more
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; The rational root theorem states that for any ... more
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; The rational root theorem states that for any ... more
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; The rational root theorem states that for any ... more
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; The rational root theorem states that for any ... more
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; The rational root theorem states that for any ... more
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{2, , } ; The rational root theorem states that ... more
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; The rational root theorem states that for any ... more
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; The rational root theorem states that for any ... more
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; The rational root theorem states that for any ... more
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; The rational root theorem states that for any ... more
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; Rational root theorem states that the if is ... more
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; Rational root theorem states that the if is ... more
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; Rational root theorem states that the if is ... more
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; Rational root theorem states that the if is ... more
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; Rational root theorem states that the if is ... more
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; The rational root theorem states that the if ... more
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; Rational root theorem states that the if is ... more
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Compare the given equation with the polynomial ... more
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Compare the given equation with the polynomial ... more
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Compare the given equation with the polynomial ... more
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Compare the given equation with the polynomial ... more
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Compare the given equation with the polynomial ... more
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; Rational root theorem states that the if is ... more
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; Rational root theorem states that the if is ... more
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; Rational root theorem states that the if is ... more
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. ; Rational root theorem states that the if is ... more
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1 positive and 1 negative real solution ; ... more
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2 positive real solutions ; Descartes’s rule of ... more
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1 positive real solution and 2 non real complex ... more
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1 negative real solution and 2 non real complex ... more
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2 positive and 1 negative real solution or 1 ... more
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2 negative and 1 positive real solution or 1 ... more
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5 positive real solutions or 3 positive and 2 non ... more
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2 positive real solutions, 1 negative real ... more
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1 negative real solution and 4 non real complex ... more
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1 positive real solution,1 negative real solution ... more
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The multiplicity 2 of the solution of the given ... more
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Compare the given equation with the polynomial ... more
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Consider an equation , whose root is .Compare the ... more
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Consider an equation , whose root is .Compare the ... more
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Non real complex solutions of the polynomial ... more
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The principle of zero product states that if , ... more
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Factor the polynomial .Take common from the ... more
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The rational zero theorem states that if is a ... more
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The graph of the function lies below the - axis ... more
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The zeros of the polynomial function satisfies the... more
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The graph of the function is determined by:If is... more
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Since the complex roots always occur in pairs, and... more
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The definition of the turning points states that ... more
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Equate the given polynomial function to 0 to ... more
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Equate the given polynomial function to 0 to ... more
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Equate the given polynomial function to 0 to ... more
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Equate the given polynomial function to 0 to ... more
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Equate the given polynomial function to 0 to ... more
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Equate the given polynomial function to 0 to ... more
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Equate the given polynomial function to 0 to ... more
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Substitute , 0, 1 and 2 for to obtain the ... more
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Substitute , , , 0 and 0.5 for to obtain the ... more
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Equate the given polynomial function to 0 to ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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The -intercept of a function is obtained by ... more
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1.7 inches ; Consider as the length of the square... more
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32 units ; Use the graphing calculator to graph ... more
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There are no positive solutions because the given ... more
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Since the given function is the product of two ... more
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The second function can be obtained by shifting ... more
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The zero product rule is defined as that if , then... more
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The second function will be the reflection of the ... more
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The graph of the third function will be closer to ... more
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The graph of the third function will be closer to ... more
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The vertical asymptote is the vertical line where ... more
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The vertical asymptote is the vertical line where ... more
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The function is said to be symmetric about the ... more
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The vertical asymptote of the given function is ... more
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The domain of a rational function is the set of ... more
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A vertical line at is called the vertical ... more
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A vertical line at is called the vertical ... more
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The horizontal line is called a horizontal ... more
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The horizontal line is called a horizontal ... more
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An example of the rational function without ... more
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; A vertical line at is called the vertical ... more
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; A vertical line at is called the vertical ... more
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; A vertical line at is called the vertical ... more
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; A vertical line at is called the vertical ... more
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; ; A vertical line at is called the vertical ... more
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; ; A vertical line at is called the vertical ... more
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; ; A vertical line at is called the vertical ... more
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; ; A vertical line at is called the vertical ... more
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No vertical asymptote, Horizontal asymptote: ; A ... more
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No vertical asymptote, Horizontal asymptote: ; A ... more
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The horizontal line is called a horizontal ... more
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The horizontal line is called a horizontal ... more
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The horizontal line is called a horizontal ... more
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The horizontal line is called a horizontal ... more
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The horizontal line is called a horizontal ... more
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The horizontal line is called a horizontal ... more
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The horizontal line is called a horizontal ... more
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The horizontal line is called a horizontal ... more
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The horizontal line is called a horizontal ... more
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The horizontal line is called a horizontal ... more
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The horizontal line is called a horizontal ... more
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The horizontal line is called a horizontal ... more
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The horizontal line is called a horizontal ... more
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The horizontal line is called a horizontal ... more
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The horizontal line is called a horizontal ... more
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The horizontal line is called a horizontal ... more
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An asymptote is a line that a curve approaches but... more
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Equate the denominator of the rational function to... more
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From the graph it can be seen that as gets larger... more
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The graph does not show the oblique asymptote. ; ... more
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A function is symmetric about the axis if and ... more
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A function is symmetric about the axis if and ... more
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A function is symmetric about the axis if and ... more
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A function is symmetric about the axis if and ... more
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A function is symmetric about the axis if and ... more
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A rational function is of the form , where .... more
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A rational function is of the form , where .The ... more
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A rational function is of the form , where .A ... more
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A rational function is of the form , where .A ... more
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A rational function is of the form , where .The ... more
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A rational function is of the form , where .A ... more
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; The oblique asymptote of the given rational ... more
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; The oblique asymptote of the given rational ... more
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; The oblique asymptote of the given rational ... more
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; The oblique asymptote of the given rational ... more
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; The oblique asymptote of the given rational ... more
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; The oblique asymptote of the given rational ... more
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A function is symmetric about the axis if and ... more
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A function is symmetric about the axis if and ... more
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A function is symmetric about the axis if and ... more
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The given function is neither symmetric about the... more
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A function is symmetric about the axis if and ... more
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The given function is symmetric about the origin. ... more
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The given function is neither symmetric about the... more
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The given function is neither symmetric about the... more
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The given function is neither symmetric about the... more
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The given function is neither symmetric about the... more
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The given function is symmetric about the origin. ... more
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The given function is symmetric about the origin. ... more
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The given function is symmetric about the origin. ... more
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The given function is symmetric about the origin. ... more
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The given function is neither symmetric about the... more
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The given function is neither symmetric about the... more
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The given function is neither symmetric about the... more
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The given function is neither symmetric about the... more
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The given function is neither symmetric about the... more
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The given function is neither symmetric about the... more
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The oblique asymptote is a quotient obtained by ... more
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The function is undefined at the vertical ... more
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Calculate the points of the given function where ... more
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Equate the right-hand side of the equations for ... more
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, 6. ; Multiply the expression by and place ... more
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Quotient ; Remainder ; The coefficients of the ... more
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276 ; Consider the given function as dividend and ... more
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Consider the given function as dividend and 2 as ... more
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The given equation has a solution of of ... more
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The given equation has either three positive and ... more
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Consider a function . ; The given function has a ... more
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Factorize the given polynomial.Take out as a ... more
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, . ; Solve the denominator of the given function ... more
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The line is the horizontal asymptote. ; Divide ... more
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The line is the oblique asymptote. ; Use the ... more
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Since , the given graph is symmetric with respect ... more
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Q: ; R: 3 ; The coefficients of the dividend are 3... more
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Q: ; R:16 ; The coefficients of the dividend are 5... more
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Q: ; R: ; The coefficients of the dividend are , 1... more
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Quotient ; Remainder ; The dividend can be written... more
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1 ; Substitute 1 for in the given function and ... more
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; Substitute for in the given function and ... more
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20 ; Substitute for in the given function and ... more
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0 ; Consider the given function as dividend and 8 ... more
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The factor theorem states that a polynomial has a... more
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The factor theorem states that a polynomial has a... more
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The factor theorem states that a polynomial has a... more
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The factor theorem states that a polynomial has a... more
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; Consider a polynomial equation in which the ... more
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; Consider a polynomial equation in which the ... more
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; Consider a polynomial equation in which the ... more
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; Consider a polynomial equation in which the ... more
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The given polynomial has two variations of signs... more
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The given polynomial has no variations of signs. ... more
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Substitute the values of as 0, 1, 2, 3 and 4 in ... more
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Zeros of a function are the points where the ... more
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Factor out from the given polynomial.The ... more
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Factorise the given polynomial.Rewrite as and ... more
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The vertical asymptote of a rational function is a... more
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The vertical asymptote of a rational function is a... more
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Consider the denominator of the given function. In... more
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The vertical asymptote of a rational function is a... more
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Remainder: 0,Quotient: . ; The coefficients of the... more
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Remainder: 38,Quotient: ; The coefficients of the ... more
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; Divide the given polynomial by .The value of ... more
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5 ; Divide the given polynomial by .The value of ... more
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39 ; Divide the given polynomial by .The value of... more
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The factor theorem states has a factor if and ... more
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The factor theorem states has a factor if and ... more
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The factor theorem states has a factor if and ... more
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The factor theorem states has a factor if and ... more
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; The rational root theorem states for a given ... more
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; The rational root theorem states for a given ... more
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; The rational root theorem states for a given ... more
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. ; The rational root theorem states for a given ... more
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; The rational root theorem states for a given ... more
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The given polynomial has two real roots, one ... more
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0; ; ; The -intercept is the point where the graph... more
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; The vertical asymptotes of the graph of a ... more
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; A line is a horizontal asymptote of the graph... more
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Symmetric with respect to the -axis ; If for a ... more
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Symmetric with respect to the origin ; If for a ... more
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Solve to obtain the zeros of the given polynomial... more
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Solve to obtain the zeros of the given polynomial... more
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Equate the denominator of the given function with ... more
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Compare the given equation with the polynomial ... more
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The horizontal line is called a horizontal ... more
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The horizontal line is called a horizontal ... more
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The horizontal line is called a horizontal ... more
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The horizontal line is called a horizontal ... more
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The horizontal line is called a horizontal ... more
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The horizontal line is called a horizontal ... more