# Factoring Monomials

The easiest way to factor a polynomial, and the first thing you should look for, is factoring out a monomial. This is a simple matter of looking for everything the parts of the polynomial have in common. So, if I asked you to factor

*xy* + *x*^{2}

You would start by looking at the two terms of the polynomial and noticing that they both have an *x* term. If you take an *x* away from the first term, all that's left is the *y*. Remember that *x*^{2} = *x* · *x*, so if you take an *x* away from it all that's left is the second *x*. This makes our factored polynomial

*x* (*y* + *x*)

Here's a more complicated example. Factor

*x*^{3}*y*^{2} + *x*^{2}*y*

Both of the terms have an *x* but we can actually do better. When you're looking for things in common you should always look for the smallest exponent. In this case, both of our terms have an *x*^{2} in common. If we take that out of both terms we get

*x*^{2}(*x**y*^{2} + *y*)

But we're not done yet. Notice that both terms have a *y* part. If we factor that out as well, we get our final answer.

*x*^{2}*y*(*x**y* + 1)

Notice that I left a 1 behind when I took the *y* out of the second term. That's because you can think of the original *y* as 1 · *y*.