# Homework Help: Factorization of a complex polynomial

1. Apr 23, 2012

### hoopsmax25

1. The problem statement, all variables and given/known data
p(x)=((x−1)^2 −2)^2 +3. From here find the full factorization of p(x) into the product of first order terms and identify all the
complex roots.

2. Relevant equations
I am having trouble doing this by hand. I know there are four complex roots but can't seem to figure out how to get them factored out.

3. The attempt at a solution

2. Apr 23, 2012

### SammyS

Staff Emeritus
Solve $\displaystyle ((x−1)^2 −2)^2 +3 = 0$ in steps.

First solve for $\displaystyle ((x−1)^2 −2)\,.$ There are two solutions.

Then isolate $\displaystyle (x−1)^2$ for each of the above solutions and take the square root of both sides in each case.