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§ 5.6

§ 5.6. A General Factoring Strategy. A Strategy for Factoring Polynomials, page 363. ///////////////////////////////////////////. Blitzer, Intermediate Algebra , 5e – Slide # 2 Section 5.6. Factoring a Polynomial. EXAMPLE. Factor:. SOLUTION.

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§ 5.6

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  1. §5.6 A General Factoring Strategy

  2. A Strategy for Factoring Polynomials, page 363 /////////////////////////////////////////// Blitzer, Intermediate Algebra, 5e – Slide #2 Section 5.6

  3. Factoring a Polynomial EXAMPLE Factor: SOLUTION 1) If there is a common factor, factor out the GCF. Because 2y is common to both terms, we factor it out. Factor out the GCF 2) Determine the number of terms and factor accordingly. The factor has two terms. This binomial can be expressed as , so it can be factored as the difference of two squares. Blitzer, Intermediate Algebra, 5e – Slide #3 Section 5.6

  4. Factoring a Polynomial CONTINUED Rewrite as the difference of two squares Factor 3) Check to see if factors can be factored further. We note that is the difference of two squares, , so we continue factoring. Blitzer, Intermediate Algebra, 5e – Slide #4 Section 5.6

  5. Factoring a Polynomial CONTINUED The previous factorization Rewrite last factor as the difference of two squares Factor Blitzer, Intermediate Algebra, 5e – Slide #5 Section 5.6

  6. Factoring a Polynomial EXAMPLE Factor: SOLUTION 1) If there is a common factor, factor out the GCF. Because 5 is common to both terms, we factor it out. Factor out the GCF 2) Determine the number of terms and factor accordingly. The factor has three terms and is a perfect square trinomial. We factor using . Blitzer, Intermediate Algebra, 5e – Slide #6 Section 5.6

  7. Factoring a Polynomial CONTINUED Factor out the GCF Rewrite the part in parentheses in form Factor 3) Check to see if factors can be factored further. In this case, they cannot, so we have factored completely. Blitzer, Intermediate Algebra, 5e – Slide #7 Section 5.6

  8. DONE

  9. Factoring a Polynomial We have looked at factoring out a common factor, factoring by grouping, factoring a difference of squares, factoring general trinomials using trial and error, factoring a sum or difference of cubes, and factoring other special forms. It is important when you wish to factor a polynomial to know where to start. You should always look first to see if there is a common factor that you can factor out. Do that first. Then consider the number of terms in the polynomial. Strategies for factoring a polynomial based on the number of terms in the polynomial follow. Blitzer, Intermediate Algebra, 5e – Slide #9 Section 5.6

  10. Factoring a Polynomial EXAMPLE Factor: SOLUTION 1) If there is a common factor, factor out the GCF. Because 3 is common to both terms, we factor it out. Factor out the GCF 2) Determine the number of terms and factor accordingly. The factor has two terms. This binomial can be expressed as , so it can be factored as the difference of two cubes. Blitzer, Intermediate Algebra, 5e – Slide #10 Section 5.6

  11. Factoring a Polynomial CONTINUED Rewrite as the difference of two cubes Factor Simplify 3) Check to see if factors can be factored further. In this case, they cannot, so we have factored completely. Blitzer, Intermediate Algebra, 5e – Slide #11 Section 5.6

  12. Factoring Strategy • Is there a common factor? If so, factor out the GCF. • How many terms?If two terms • The difference of two squares • The sum of two cubes • The difference of two cubes • If three terms • A perfect square trinomial • If a is equal to 1, use the trial-and-check. • If a is > than 1, use the grouping method. • If it has four or more terms, factor by grouping

  13. A Strategy for Factoring Polynomials CONTINUED Blitzer, Intermediate Algebra, 5e – Slide #13 Section 5.6

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