Solve the following equation using synthetic division, given the indicated root.

$\displaystyle

x^3-10x^2 + 28x-24=0,r=2

$

Synthetic Division using the given root:

$\displaystyle

x^3-10x^2+28x-24=(x+2)(x^2-8x+12)

$

$\displaystyle

(x^2-8x+12)=(x-6)(x-2)

$

Solution:

$\displaystyle

(x+2)(x-6)(x-2)

$

I know my solution is wrong because multiplying back in does not result in the original answer.

What am I doing wrong?

I think that I'm performing an error in the begining with the synthetic division but I can't tell what I'm doing wrong.