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How to Factor an Expression Taking out the Greatest Common Factor

You can factor a quadratic expression to make it easier to work with. Some quadratic expressions can be made better by finding a greatest common factor (GCF). If the terms in the quadratic expression have something in common, then that can be factored out, leaving the expression easier to deal with.

Example 1: Factor the quadratic expression,

image0.png
  1. Rewrite the expression in decreasing powers of x.

    image1.png
  2. Find the GCF.

    Although the expression contains large numbers, each number can be evenly divided by 800.

  3. Factor out the GCF.

    image2.png

Example 2: Factor the quadratic expression:

image3.png

This more complicated example uses four different variables with powers of 2.

  1. Rewrite the expression in decreasing powers of x.

    Only the x appears in a term with a power of one. So, you may choose to write this as a quadratic in x.

    image4.png
  2. Find the GCF.

    image5.png
  3. Factor out the GCF.

    image6.png
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