Question

Is it possible to factor `y=2x^3-2x^2+2x-2`? If so, what are the factors?

Answer 1

Yes, it is possible to factor this. Here is what I did:

Explanation:

`y = 2x^3-2x^2+2x-2`

`y = 2x^2(x-1) + 2(x-1)`

`y = (2x^2+2)(x-1)`

The factors are `(2x^2+2)` and `(x-1)`.

Answer 2

`y=2(x^2+1)(x-1)`

Explanation:

`y=2x^3-2x^2+2x-2`
Greatest common factor:
`y=2*(x^3-x^2+x-1)`
Factor by grouping:
`y=2*((x^3-x^2)+(x-1))`
`y=2*(x^2*(x-1)+1*(x-1))`
`y=2*(x^2+1)*(x-1)`
Thus, the factors are `2`, `(x^2+1)`, and `(x-1)`
graph{2x^3-2x^2+2x-2 [-10, 10, -5, 5]}