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§ 5.5

§ 5.5. Factoring Special Forms. A Strategy for Factoring Polynomials, page 363. ///////////////////////////////////////////. Blitzer, Intermediate Algebra , 5e – Slide # 2 Section 5.6. The Difference of Two Squares. P 353. Blitzer, Intermediate Algebra , 5e – Slide # 3 Section 5.5.

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§ 5.5

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  1. §5.5 Factoring Special Forms

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

  3. The Difference of Two Squares P 353 Blitzer, Intermediate Algebra, 5e – Slide #3 Section 5.5

  4. The Difference of Two Squares EXAMPLE Factor: SOLUTION We must express each term as the square of some monomial. Then we use the formula for factoring Express as the difference of two squares Factor using the Difference of Two Squares method Blitzer, Intermediate Algebra, 5e – Slide #4 Section 5.5

  5. The Difference of Two Squares Check Point 1a Factor Check Point 1b Factor P 354 Blitzer, Intermediate Algebra, 5e – Slide #5 Section 5.2

  6. The Difference of Two Squares EXAMPLE Factor: SOLUTION The GCF of the two terms of the polynomial is 6. We begin by factoring out 6. Factor the GCF out of both terms Factor using the Difference of Two Squares method Blitzer, Intermediate Algebra, 5e – Slide #6 Section 5.5

  7. The Difference of Two Squares Check Point 2 Factor P 355 Blitzer, Intermediate Algebra, 5e – Slide #7 Section 5.2

  8. The Difference of Two Squares EXAMPLE Factor completely: SOLUTION Express as the difference of two squares The factors are the sum and difference of the expressions being squared The factor is the difference of two squares and can be factored Blitzer, Intermediate Algebra, 5e – Slide #8 Section 5.5

  9. The Difference of Two Squares CONTINUED The factors of are the sum and difference of the expressions being squared Thus, Blitzer, Intermediate Algebra, 5e – Slide #9 Section 5.5

  10. The Difference of Two Squares Check Point 3 Factor P 355 Blitzer, Intermediate Algebra, 5e – Slide #10 Section 5.2

  11. Factoring Completely EXAMPLE Factor completely: SOLUTION Group terms with common factors Factor out the common factor from each group Factor out x + 3 from both terms Factor as the difference of two squares Blitzer, Intermediate Algebra, 5e – Slide #11 Section 5.5

  12. The Difference of Two Squares Check Point 4 Factor P 355 Blitzer, Intermediate Algebra, 5e – Slide #12 Section 5.2

  13. Factoring Special Forms P 356 Blitzer, Intermediate Algebra, 5e – Slide #13 Section 5.5

  14. Factoring Perfect Square Trinomials EXAMPLE Factor: SOLUTION We suspect that is a perfect square trinomial because . The middle term can be expressed as twice the product of 4x and -5y. Express in form Factor Blitzer, Intermediate Algebra, 5e – Slide #14 Section 5.5

  15. Factoring Perfect Square Trinomials Check Point 5a Factor Check Point 5b Factor Check Point 5b Factor P 357 Blitzer, Intermediate Algebra, 5e – Slide #15 Section 5.2

  16. Grouping & Difference of Two Squares EXAMPLE, use for #65 and #67 (not on test) Factor: SOLUTION Group as minus a perfect square trinomial to obtain a difference of two squares Factor the perfect square trinomial Rewrite as the difference of two squares Blitzer, Intermediate Algebra, 5e – Slide #16 Section 5.5

  17. Grouping & Difference of Two Squares CONTINUED Factor the difference of two squares. The factors are the sum and difference of the expressions being squared. Simplify Thus, Blitzer, Intermediate Algebra, 5e – Slide #17 Section 5.5

  18. DONE

  19. The Difference of Two Squares Check Point 6 Factor Check Point 7 Factor P 357-8 Blitzer, Intermediate Algebra, 5e – Slide #19 Section 5.2

  20. Special Polynomials In this section we will consider some polynomials that have special forms that make it easy for us to see how they factor. You may look at a polynomial and say, “Oh, that’s just a difference of squares” or “I think we have a sum of cubes here.” When you have a special polynomial, in particular one that is a difference of two squares, a perfect square polynomial, or a sum or difference of cubes, you will have a factoring formula memorized and will know how to proceed. That’s why these polynomials are “special”. They may just become our best friends among the polynomials.…. Blitzer, Intermediate Algebra, 5e – Slide #20 Section 5.5

  21. The Sum & Difference of Two Cubes Blitzer, Intermediate Algebra, 5e – Slide #21 Section 5.5

  22. The Sum & Difference of Two Cubes EXAMPLE Factor: SOLUTION Rewrite as the Sum of Two Cubes Factor the Sum of Two Cubes Simplify Thus, Blitzer, Intermediate Algebra, 5e – Slide #22 Section 5.5

  23. The Sum & Difference of Two Cubes EXAMPLE Factor: SOLUTION Rewrite as the Difference of Two Cubes Factor the Difference of Two Cubes Simplify Thus, Blitzer, Intermediate Algebra, 5e – Slide #23 Section 5.5

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