factorise

The given polynomial is 2y³ + y² – 2y -1

y = 1 is a root of this polynomial.

Then dividing the polynomial by y – 1, we get the quotient as 2y² + 3y + 1.

Now we solve this quadratic polynomial by splitting its middle term.

2y² + 3y + 1 = 2y² + 2y + y + 1

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

                  = (y + 1) (2y + 1)

So, the factors of the given polynomial 2y³ + y² – 2y -1 are = (y – 1) (y + 1) (2y + 1)