# Homework Help: Factors of a polynomial

1. Oct 16, 2008

### phyguy321

1. The problem statement, all variables and given/known data
Prove that every polynomial with real coefficients factors into linear and quadratic real factors.

2. Relevant equations
So show that f(x) = x$$^{n}$$ + a$$_{}n-1$$x$$^{n-1}$$+...+ax +a$$_{}0$$ factors into some (x-r$$_{}1$$)(x$$^{2}$$+4)......

3. The attempt at a solution
I understand how and why this is true but could someone point me in the right direction on where to start?

Last edited: Oct 16, 2008
2. Oct 16, 2008

### Dick

If all of the roots r_i are real then you are done. Suppose there is a factor (x-a) with 'a' complex? You can match that up with another factor so that the product is a real quadratic. What's that other factor and how do you know it exists?