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:

Concept:

(x - 5)

is a factor, then the cubic polynomial can be expressed as

(x - 5)

times a quadratic expression.

Explanation:

Rewrite the polynomial by grouping terms so that

(x - 5)

can be factored out.

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)

Now factor the quadratic

x^2 + x - 6

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

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

= (x + 3)(x - 2)

Thus, the remaining factors are

(x + 3)

and

(x - 2)

Answer:

Option A:

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

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