# How do you factor #f(x)=x^3-12x^2+36x-32# completely, given that (x-2) is a factor?

##### 1 Answer

Dec 2, 2016

#### Explanation:

Knowing that

2.....|.......1.........-12.........+36.........-32

........|...................2..........-20.........+32

........|.......1.........-10..........+16...........0

and find:

We could use the quadratic formula to find the factors of

or go simply by inspection:

1) q(x) has two changes in sign, so it has two positive real roots.

2) The product of the roots is

3) the sum of the roots is

It's easy to see that