# Thread: Solve using Synthetic Division and the Given Root

1. ## Solve using Synthetic Division and the Given Root

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.

2. The root is 2 NOT -2...

3. Originally Posted by MauiCormac
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:

$\displaystyle x^3-10x^2+28x-24=(x+2)(x^2-8x+12)$
You are wrong here: if x= 2 is a root then x- 2 is a factor, not x+ 2.

$\displaystyle (x^2-8x+12)=(x-6)(x-2)$

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.

4. I know.

I got it. Somone just explained it to me. The root is 2 which is one answer, and then when I solve I get (x-6)(x-2) and I forgot to make that = to 0.