# Thread: Factoring Polynomials using Synthetic Division

1. ## Factoring Polynomials using Synthetic Division

Hi,

I am hearing synthetic division for the first time today!

Can anyone be kind enough to explain to me what "synthetic division"? And how I can use that to solve the following:

The question says, “use synthetic division to determine if (x + 1) is a factor of P(x) = x^4 + 3x^3 - 2x^2 -12x - 8.If so, write P(x) as (x+1) times the reduced polynomial. Then find the zeros of P(x) (with multiplicity)

Thanks

3. ## Re: Factoring Polynomials using Synthetic Division

I think it's good you look for some examples on the internet.

If $\displaystyle (x+1)$ is a divisor of $\displaystyle P(x)$ then $\displaystyle P(x)$ can be factored as:
$\displaystyle P(x)=(x+1)\cdot(ax^3+bx^2+cx+d)$

With the method of synthetic division you'll be able to find $\displaystyle ax^3+bx+c+d$ and if you apply again synthetic division you'll be able to factore: $\displaystyle ax^3+bx+c+d=(x-a)(x^2+ax+b)$.

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