Question

Factarise: 2y^3 +y²-2y-1.​

Answer 1

Answer:

2y³+y²-2y-1=(y-1)(y+1)(2y+1)

Step-by-step explanation:

By trail , we find that,

p(1) = 2(1)³+1²-2(1)-1

= 2+1-2-1

= 0

By Factor theorem,

(y-1) is a factor of p(y).

Now,

2y³+y²-2y-1

=2y²(y-1)+3y(y-1)+1(y-1)

=(y-1)(2y²+3y+1)

=(y-1)(2y²+2y+1y+1)

=(y-1)[2y(y+1)+1(y+1)]

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

Therefore,

2y³+y²-2y-1=(y-1)(y+1)(2y+1)

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