Factor Theorem (AQA A-Level Mathematics): Quizzes

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Factor Theorem
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According to the Remainder Theorem, what is the remainder when f(x)f(x) is divided by (x−a)(x - a)?

f(a)f(a)

What condition must be satisfied for (x−a)(x - a) to be a factor of polynomial f(x)f(x)?

f(a)=0f(a) = 0

Find the remainder when x3+8x2−6x+2x^3 + 8x^2 - 6x + 2 is divided by x+6x + 6.

110

What value of xx should be substituted when finding remainder for division by 3x−23x - 2?

23\frac{2}{3}

For g(x)=2x3+x2−13x+6g(x) = 2x^3 + x^2 - 13x + 6, what is g(−3)g(-3)?

0

What are the solutions to g(x)=0g(x) = 0 where g(x)=(x+3)(2x−1)(x−2)g(x) = (x + 3)(2x - 1)(x - 2)?

x=−3,12,2x = -3, \frac{1}{2}, 2

To check if (x−2)(x - 2) is a factor of f(x)f(x), what value should be substituted?

x=2x = 2

What does it mean if f(a)=0f(a) = 0 for a polynomial f(x)f(x)?

(x−a)(x - a) is a factor

Given (x+1)(x + 1) and (x−2)(x - 2) are factors of cx3+dx2−9x−10cx^3 + dx^2 - 9x - 10, find cc and dd.

c=2,d=3c = 2, d = 3

What is the complete factorization of 2x3+3x2−18x+82x^3 + 3x^2 - 18x + 8?

(x−2)(2x−1)(x+4)(x - 2)(2x - 1)(x + 4)

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