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