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Mastering Polynomial Factoring Techniques

Learn how to simplify polynomials and find the greatest common factor in pairs of monomials. Practice factoring through examples and step-by-step explanations. Improve your math skills with this essential lesson.

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Mastering Polynomial Factoring Techniques

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  1. Classwork: 01/23/17 1. 2(w + 1) 2. 3x(x2 – 4) Simplify. Find the GCF of each pair of monomials. 3. 4h2 and 6h

  2. Essential Questions How do you factor polynomials by using the greatest common factor?

  3. Writing Math Aligning common factors can help you find the greatest common factor of two or more terms.

  4. Example 1A: Factoring by Using the GCF Factor each polynomial. Check your answer. 2x2– 4 2x2 = 2 x  x Find the GCF. 4 = 2  2 The GCF of 2x2 and 4 is 2. 2 2x2–(2  2) 2(x2– 2) Check 2(x2– 2) The product is the original polynomial.  2x2– 4

  5. Example: Factoring by Using the GCF 8x3– 4x2– 16x 8x3 = 2  2  2  x  x  x Find the GCF. 4x2 = 2  2  x  x 16x = 2  2  2  2 x The GCF of 8x3, 4x2, and 16x is 4x. 2  2 x = 4x 4x(2x2–x– 4) Check 4x(2x2–x– 4) The product is the original polynomials. 8x3– 4x2– 16x 

  6. Example: Factoring by Using the GCF 3x3 + 2x2– 10 3x3 = 3 x x x Find the GCF. 2x2 = 2 x x 10 = 2 5 There are no common factors other than 1. 3x3 + 2x2– 10 The polynomial cannot be factored further.

  7. Example: Factoring Out a Common Binomial Factor A. 5(x + 2) + 3x(x + 2) Factor out (x + 2). (x + 2)(5 + 3x) B. –2b(b2 + 1)+ (b2 + 1) (b2 + 1)(–2b + 1) Factor out (b2 + 1).

  8. Example: Factoring Out a Common Binomial Factor Factor each expression. C. 4z(z2–7) + 9(2z3 + 1) There are no common factors. 4z(z2–7) + 9(2z3 + 1) The expression cannot be factored. Leave it the same way as the final answer

  9. You may be able to factor a polynomial by grouping. When a polynomial has four terms, you can make two groups and factor out the GCF from each group.

  10. Example: Factoring by Grouping 6h4– 4h3 + 12h– 8 Group terms that have a common number or variable as a factor. (6h4– 4h3) + (12h– 8) 2h3(3h– 2) + 4(3h– 2) (3h– 2)(2h3 + 4) Factor out (3h – 2).  6h4– 4h3 + 12h– 8 Check (3h– 2)(2h3 + 4) =

  11. Lesson Quiz: Factor each polynomial. (byb GCF) 1. 16x + 20x3 2. 4m4 – 12m2 + 8m Factor each expression. (by grouping) 3. 7k(k – 3) + 4(k – 3) 4. 3y(2y + 3) – 5(2y + 3)

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