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:

Since f(3) = 0, then (x - 3) is a factor of f(x).

Dividing f(x) by (x - 3), we get $2x^{2} + 3x - 2$ .

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

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

Therefore, $f(x) = (x - 3)(x + 2)(2x -1)$

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