Question

Which of the following is a factor of P(y) = 2y3 - 11y2 + 12y + 9?

Answer 1

f(3) = 0  so x-3 would be a factor

Answer 2

`2y^3 - 11y^2 + 12y + 9 = (y-3)(y-3)(2y+1) = (y-3)^2(2y+1)`

Explanation:

We are given the expression:

`2y^3 - 11y^2 + 12y + 9 = 0`

We have to factor this expression.

By hit and trial method, it was found that 3 is a root of given expression.

Thus, it can be written:

`2y^3 - 11y^2 + 12y + 9 = (y-3)(2y^2 - 5y - 3)`

We can further factorize
`2y^2 - 5y - 3` by splitting the middle term technique.

`2y^2 - 5y - 3 = 0\\=2y^2 - 6y + y - 3 = 0\\2y(y-3)+1(y-3) = 0\\(y-3)(2y+1)=0`

Thus, the expression can be factorized as:

`2y^3 - 11y^2 + 12y + 9 = (y-3)(y-3)(2y+1) = (y-3)^2(2y+1)`