Solve using Synthetic Division and the Given Root

**MauiCormac** · July 12th 2010, 03:54 AM

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

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

Synthetic Division using the given root:

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

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

Solution:

$ (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.

**Also sprach Zarathustra** · July 12th 2010, 04:01 AM

The root is 2 NOT -2...

**HallsofIvy** · July 12th 2010, 04:42 AM

Originally Posted by MauiCormac

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

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

Synthetic Division using the given root:

$ 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.

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

Solution:

$ (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.

**MauiCormac** · July 12th 2010, 05:18 AM

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.

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