If (x - 5) is a factor of x³ - 4x² - 11x + 30, find the remaining factors.

Correct Answer is : (x+3) and (x−2)(x + 3) { and } (x - 2)(x+3) and (x−2)

Correct Answer is : (x+3) and (x−2)(x + 3) { and } (x - 2)(x+3) and (x−2)

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WAEC Further Mathematics 2023 Paper

Question : 40

Total: 40

(x - 5)

x^3 - 4x^2 - 11x + 30

, find the remaining factors.

Solution:

(x - 5) is a factor of $x^3 - 4x^2 - 11x + 30$ . To find the remaining factors, let's draw out $(x - 5)$ from the parent expression.

x^3 - 4x^2 - 11x + 30 = x^3 - 5x^2 + x^2 - 5x - 6x + 30

= x^2(x - 5) + x(x - 5) - 6(x - 5) = (x - 5)(x^2 + x - 6)

∴ To find the remaining factors, we factorize

(x2 + x - 6)

x^2 + x - 6 = x^2 + 3x - 2x - 6

= x(x + 3) - 2(x + 3) = (x + 3)(x - 2)

∴ The other two factors are

(x + 3) \text{ and } (x - 2)

ALTERNATIVELY

$\therefore x^2 + x - 6 = (x + 3) \text{ and } (x - 2)$

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