Given that f(x) = 2x³ - 3x² - 11x + 6 and f(3) = 0, factorize f(x).

Correct Answer is : (x - 3)(x + 2)(2x -1)

Correct Answer is : (x - 3)(x + 2)(2x -1)

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WAEC Further Mathematics 2013 Paper

Question : 9

Total: 40

Given that

f(x) = 2x^{3} - 3x^{2} - 11x + 6

f(3) = 0

, factorize f(x).

Solution:

Concept:

f(a) = 0

, then

(x - a)

is a factor of

f(x)

Explanation:

Since

f(3) = 0

(x - 3)

is a factor of

f(x)

Divide

f(x)

(x - 3)

. The quotient is

2x^{2} + 3x - 2

Factor the quadratic:

2x^{2} + 3x - 2 = 2x^{2} + 4x - x - 2

= 2x(x + 2) - 1(x + 2)

= (2x - 1)(x + 2)

Therefore,

f(x) = (x - 3)(2x - 1)(x + 2)

Answer:

f(x) = (x - 3)(x + 2)(2x - 1)

Option C.

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