Factories: ${2 y}^{3} + y^{2} - 2 y - 1$

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Solution

$2 y^{3} + y^{2} - 2 y - 1$
$y = 1$ is one root
(Image)
$2 y^{2} + 3 y + 1 = 0$
$2 y^{2} + 2 y + y + 1 = 0$
$2 y (y + 1) + 1 (y + 1) = 0$
$y = - \frac{1}{2}, - 1$
$∴ (y + 1) (y - 1) (y + \frac{1}{2})$

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2 y^{3} + y^{2} - 2 y - 1

2 y^{3} + y^{2} - 2 y - 1

Factorise :
(i) $x^{3}$ −2 $x^{2}$ −x+2
(ii) 2 $y^{3}$ + $y^{2}$ −2y−1

2 y^{3} + y^{2} - 2 y - 1 = (x + a) (x - b) (c x + d)

a + b + c + d

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