Question

factorise 2y^3+y²-2y+1

Answer 1

Step-by-step explanation:

Let p(y)=2y³+y²-2y-1

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)