Factor Theorem (Edexcel A-Level Mathematics): Quizzes

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Factor Theorem
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What is the remainder when f(x)f(x) is divided by (xa)(x-a) according to the Remainder Theorem?

f(a)f(a)

According to the Factor Theorem, if f(a)=0f(a) = 0, what can we conclude?

(xa)(x-a) is a factor of f(x)f(x)

To find the remainder when dividing by (x+6)(x+6), what value should be substituted into f(x)f(x)?

x=6x = -6

What is the remainder when x3+8x26x+2x^3 + 8x^2 - 6x + 2 is divided by x+6x+6?

110110

To use the Remainder Theorem with divisor 3x23x-2, what value of xx should be used?

x=23x = \frac{2}{3}

If g(3)=0g(-3) = 0 for polynomial g(x)g(x), which of the following is a factor?

(x+3)(x+3)

For f(x)=2x3+3x218x+8f(x) = 2x^3 + 3x^2 - 18x + 8, what is f(2)f(2)?

00

If g(x)=(x+3)(2x1)(x2)g(x) = (x+3)(2x-1)(x-2), what are the solutions to g(x)=0g(x) = 0?

x=3,12,2x = -3, \frac{1}{2}, 2

The complete factorization of 2x3+3x218x+82x^3 + 3x^2 - 18x + 8 is:

(x2)(2x1)(x+4)(x-2)(2x-1)(x+4)

If (x+1)(x+1) and (x2)(x-2) are factors of cx3+dx29x10cx^3 + dx^2 - 9x - 10, what conditions must hold?

f(1)=0f(-1) = 0 and f(2)=0f(2) = 0

Why is the Remainder Theorem described as a quicker method?

It avoids polynomial long division

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