Factoring Out a Common Monomial Factor?

Say you have a polynomial, like

3x⁴ y - 9x³ y + 12x² y2 z

and you want to factor it. Your first step is always to look for the common monomial factor. Here's how you do it.

Step 1. : Find the greatest common factor of all the coefficients. In this example the greatest common factor of 3, -9, and 12 is 3. Factor that number out of each term:

3(x⁴y - 3x³y + 4x² y² z)

Step 2. :  Look at the powers of the variables. Take x, for example. In the three terms of the polynomial, the powers of x are 4, 3, and 2. So if you want to factor out some x's from every term, the most you can factor out is 2 of them (in other words, factor out x² .)

In this example, you can also factor out a y (but only one). You can't factor out any z's, because z does not appear in every term. So here's your factorization:
3x² y(x³ -3x + 4yz)