Question

2y³ + y² − 2y − 1

Answer 1

Let  f(y) 2y³ + y² − 2y − 1 be the given polynomial.

Now, putting y = 1we get

`f(1) = 2(1)^3 + (1)^2 - 2(1) - 1 = 2 -2 -1`

        ` = 3-3 = 0`

Now,

`f(y) = 2y^2 (y - 1) + 3y(y-1)+1(y-1)`

        ` = (y -1){2y^2 + 3y +1}`

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

        ` = (y-1)(2y +1)(y +1)`

Hence (y -1),(y+1) and (2y +1)are the factors of polynomial f(y).