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Factorisation of Quadratic Polynomials

Factors of th...

Question

Factors of the polynomial $p (x) = 2 x^{3} + 3 x^{2} - 3 x - 2$ are :

(x - 1), (x + 2), (x + 3)

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(x - 1), (x + 2), (x + 4)

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(x - 1), (x + 2), (2 x + 1)

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(x - 1), (x + 2), (2 x + 3)

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Solution

The correct option is C $(x - 1), (x + 2), (2 x + 1)$
$p (x) = 2 x^{3} + 3 x^{2} - 3 x - 2 p (1) = 2 + 3 - 3 - 2 = 0 p (x) = (x - 1) (2 x^{2} + 5 x + 2) p (x) = (x - 1) (2 x^{2} + 4 x + x + 2) p (x) = (x - 1) {2 x (x + 2) + 1 (x + 2)} p (x) = (x - 1) (2 x + 1) (x + 2) p (x) = 2 x^{3} + 3 x^{2} - 3 x - 2 p (1) = 2 + 3 - 3 - 2 = 0 p (x) = (x - 1) (2 x^{2} + 5 x + 2) p (x) = (x - 1) (2 x^{2} + 4 x + x + 2) p (x) = (x - 1) {2 x (x + 2) + 1 (x + 2)} p (x) = (x - 1) (2 x + 1) (x + 2)$
So option $C$ is correct.

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