Question

Factor x^3-12x+16. Show all work.

Answer 1

Answer:
`(x-2)^(2)(x+4)`

Explanation:

For
`x^(3) - 12x + 16` we can test out different values of x until the polynomial is zero, in this case 2 works so we can use long division or seperation of terms and factoring. But to show work, I will use seperation and factor.

`x^(3) - 12x + 16 = x^(3) - 8 - 12x + 24` =
`(x-2)(x^(2)+2x+4) -12 (x-2)`

=
`(x-2)(x^(2)+2x-8)`

Then we can factor the second-degree polynomial to get
`(x-2)(x+4)(x-2)` or
`(x-2)^(2)(x+4)`