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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)
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