factors of a polynomial

[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-1x^{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?

[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?