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Factoring Techniques: Grouping and Difference of Squares

Learn how to factor polynomials using the grouping technique and the difference of squares method. Practice examples included.

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Factoring Techniques: Grouping and Difference of Squares

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  1. Factoring Polynomials

  2. Factoring Technique #3 Factoring By Grouping for polynomials with 4 or more terms

  3. 1. Group the first set of terms and last set of terms with parentheses. 2. Factor out the GCF from each group so that both sets of parentheses contain the same factors. 3. Factor out the GCF again (the GCF is the factor from step 2). Factoring By Grouping

  4. Example 1: Step 1: Group Step 2: Factor out GCF from each group Step 3: Factor out GCF again

  5. Example 2:

  6. Factoring Method #4 Factoring polynomials that are a difference of squares.

  7. A “Difference of Squares” is a binomial (*2 terms only*) and it factors like this:

  8. To factor, express each term as a square of a monomial then apply the rule...

  9. Here is another example:

  10. Try these on your own:

  11. Answers • 1. • 2. • 3.

  12. Homework Factor by grouping 1. xy+2y+3x+6 2. 4x3+2x2-2x-2 3. 2x3-3x2-2x+3 4. 2x2+ay-ax2-2y 5. 24x3-6x2+8x-2 6. 9x3+36x2-4x-16 Factor by finding the difference of perfect squares 1. x2-81 2. y2-z2 3. 36x2-1 4. 1-4z2 5. 25m2-9n2 6. x6-36 7. y4-144 8. x8-y10 9. x2n-1 10. y2-1

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