Which of the following represents factors of the cubic polynomial, $2 x^{3} + x^{2} - 2 x - 1 ?$

[1 Mark]

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

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

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

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

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Solution

The correct option is D $(x - 1), (x + 1), (2 x + 1)$
$2 x^{3} + x^{2} - 2 x - 1 = x^{2} (2 x + 1) - 1 (2 x + 1)$

$= (x^{2} - 1) (2 x + 1)$

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

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Which of the following represents factors of the cubic polynomial, 2x3+x2−2x−1? [1 Mark]

The correct option is D (x−1),(x+1),(2x+1)2x3+x2−2x−1=x2(2x+1)−1(2x+1) =(x2−1)(2x+1) =(x−1)(x+1)(2x+1)

Which of the following represents factors of the cubic polynomial, $2 x^{3} + x^{2} - 2 x - 1 ?$

[1 Mark]

The correct option is D $(x - 1), (x + 1), (2 x + 1)$
$2 x^{3} + x^{2} - 2 x - 1 = x^{2} (2 x + 1) - 1 (2 x + 1)$

$= (x^{2} - 1) (2 x + 1)$

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