Question

11.Factorise the polynomial​

Answer 1

Step-by-step explanation:

Factorisation :

2y³ + y² - 2y -1

= y² ( 2y+1 ) -1 ( 2y+1)

= (y²-1) (2y+1)

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Answer 2

Answer:

$(y + 1)(y - 1)(2y + 1)$

Step-by-step explanation:

From factor theorem, it is seen that (y + 1) is a factor of given polynomial.

Now split the terms of polynomial so as to factor out ( y + 1 ).

$2 {y}^{3} + {y}^{2} - 2y - 1 \\ \\ = 2 {y}^{3} + 2 {y}^{2} - {y}^{2} - y - y - 1$

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

After factoring out ( y + 1 ) , factorise the quadratic obtained.

$= (y + 1)(2 {y}^{2} - y - 1) \\ \\ = (y + 1)(2 {y}^{2} - 2y + y - 1)$

$(y + 1)(2y(y - 1) + 1(y - 1)) \\ \\ = (y + 1)(y - 1)(2y + 1)$

Hope it helps