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c Check if (x + 5) is a factor of the given polynomial 5x^{3} + x^{2}  7x  5. c

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c Evaluate f(x) at x = 2, by synthetic division. f(x) = x^{4}  5x^{3} + 2x^{2} + 4x  5 c

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c Evaluate f(x) at x = 5, by synthetic division. f(x ) = x^{3}  3x^{2} + 2x + 3 c

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c Check if (x  8) is a factor of the given polynomial x^{3} + x^{2}  64x  64. c

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c x + 3 is a factor of the polynomial x^{3}  2x^{2}  11x + 12. Find the other factors. c

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c a + 5 is a factor of the polynomial 9a^{3} + 63a^{2} + 99a + 45. Find the other factors. c

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c If y  3 is a factor of the polynomial, then factor the polynomial, 9y^{3}  27y^{2}  16y + 48 completely. c

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c If m + 6 is a factor of the polynomial, then factor m^{3} + 7m^{2}  36 completely. c

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c t + 7 and t  8 are the factors of the polynomial, t^{4}  2t^{3}  85t^{2} + 86t + 1680. Factor the polynomial completely. c

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c Which of the following is a polynomial whose factors are 6y  1, y + 5 and y  5? c

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c Which of the following is a polynomial whose factors are y  7, y + 10 and y  8? c

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c Choose the polynomial whose factors are c + 15 , c  4 and c + 7. c

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c Choose the polynomial whose factors are z  14 , z + 4 and z  4. c

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c Choose the polynomial whose factors are b + 6, b  26 and b + 26? c

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c Check if (x  9) is a factor of the given polynomial x^{3} + x^{2}  81x  81. c

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c Check if (x + 10) is a factor of the given polynomial 10x^{3} + x^{2}  7x  10. c

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c Evaluate f(x) at x = 4, by synthetic division. f(x) = x^{4}  4x^{3} + 5x^{2} + 4x  9 c

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c Evaluate f(x) at x = 5, by synthetic division. f(x ) = x^{3}  2x^{2} + 2x + 9 c

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c x + 5 is a factor of the polynomial x^{3}  8x^{2}  35x + 150. Find the other factors. c

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c a + 6 is a factor of the polynomial 64a^{3} + 464a^{2} + 505a + 150. Find the other factors. c

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c If y  5 is a factor of the polynomial, then factor the polynomial, 4y^{3}  20y^{2}  9y + 45 completely. c

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c If m + 12 is a factor of the polynomial, then factor m^{3} + 13m^{2}  144 completely. c

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c t + 6 and t  7 are the factors of the polynomial, t^{4}  2t^{3}  61t^{2} + 62t + 840. Factor the polynomial completely. c

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c Which of the following is a polynomial whose factors are 3z  1, z + 2 and z  2? c

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c Which of the following is a polynomial whose factors are x  5, x + 6 and x  4? c

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c Choose the polynomial whose factors are a + 15 , a  7 and a + 10. c

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c Choose the polynomial whose factors are b  12 , b + 5 and b  5. c

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c Choose the polynomial whose factors are y + 7, y  37 and y + 37? c

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c Write a polynomial whose factors are 2x + 3, x + i and x  i. c

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c Write a polynomial whose factors are x + 2, x + 2i and x  3i. c

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c Alice expressed three consecutive odd integers in a distinct way. The product of the three integers is given by the polynomial x^{3}  9x^{2} + 23x  15. One of her integers is expressed as x  3. Find the other expressions did Alice use for the other two integers. c

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c Tim expresses the product of four numbers as x^{4}  19x^{2}  30x. Two numbers were represented by x and x + 2. Find the expressions that were used to represent the other two numbers. c

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c x  4i is a factor of the polynomial x^{3} + 3x^{2} + 16x + 48. Factor completely. c

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c x  (4  3i)is a factor of the polynomial x³  10x² + 41x  50. Factor completely. c

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c The volume of a box is given by the expression (125x^{3}  150x^{2} + 55x  6) cm^{3}. Its height is (5x  2) cm. What expressions are used to represent the other two dimensions? c

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c Is the first polynomial, a factor of the second polynomial? y  5; y^{3}  11y^{2} + 34y  20 c

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c x  2 and x  4 are factors of x^{4}  2x^{3}  13x^{2} + 14x + 24. Find the other factors. c

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c Write a polynomial with given factors: x + 2, x  2, x + 3 c

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c If the product of three binomials is x^{3} + 3x^{2}  10x  24. If one is x + 2, what are the other two binomials? c

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c Use the synthetic division, to find whether the first polynomial is a factor of the second polynomial and factor completely the second polynomial: x + 2i; x^{3} + 3x^{2} + 4x + 12 c

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