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

2

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Solution

The correct option is B $5$
We have, $2 y^{3} + y^{2} - 2 y - 1$
$w e c a n c l e a r l y s e e y = 1 i s o n e o f t h e z e r o e s$
$= (y - 1) (2 y^{2} + 3 y + 1) = (y - 1) [2 y^{2} + 2 y + y + 1]$
$= (y - 1) [2 y (y + 1) + 1 (y + 1)]$
$= (y - 1) (y + 1) (2 y + 1)$
$= (y + 1) (y - 1) (2 y + 1)$
$∴ a = 1, b = 1, c = 2 a n d d = 1$
$∴ a + b + c + d = 5$

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If 2y3+y2−2y−1=(x+a)(x−b)(cx+d).Find a+b+c+d

The correct option is B 5We have, 2y3+y2−2y−1wecanclearlyseey=1is oneofthezeroes=(y−1)(2y2+3y+1)=(y−1)[2y2+2y+y+1]=(y−1)[2y(y+1)+1(y+1)]=(y−1)(y+1)(2y+1)=(y+1)(y−1)(2y+1)∴a=1,b=1,c=2andd=1∴a+b+c+d=5

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