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Warm-Up: November 9, 2011

Warm-Up: November 9, 2011. Simplify the following:. Homework Questions?. Factoring Polynomials. Section 5-4. Factoring. Factoring is the process of writing a polynomial as the product of two or more polynomials. Prime polynomials cannot be factored using integer coefficients.

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Warm-Up: November 9, 2011

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  1. Warm-Up: November 9, 2011 • Simplify the following:

  2. Homework Questions?

  3. Factoring Polynomials Section 5-4

  4. Factoring Factoring is the process of writing a polynomial as the product of two or more polynomials. Prime polynomials cannot be factored using integer coefficients. Factormeans keep factoring until everything is prime

  5. Factoring Methods (page 239)

  6. Factoring out the Greatest Common Factor 3a2 – 12a 3a is the GCF Find the greatest common factor (GCF) of all terms. Divide each term by the greatest common factor. Write the GCF outside parentheses, with the rest of the divided terms added together inside

  7. You-Try #1: Factor a. 18x3 + 27x2 b. x2(x + 3) + 5(x + 3)

  8. Factor by Grouping • Works with an even number of terms. • Split the terms into two groups. • Factor each group separately using GCF. • To factor by grouping, the part inside parentheses of each group must be the same. • Treat the parentheses as common factors to finish factoring.

  9. Example 2: Factor

  10. You-Try #2: Factor

  11. Factoring x2 + bx + c • Look for integers r and s such that: • r × s = c • r + s = b c r s b

  12. Example 3

  13. You-Try #3

  14. Warm-Up: November 10, 2011 • Factor:

  15. Factoring ax2 + bx + c • Look for integers r and s such that: • r × s = ac • r + s = b • Divide r and s by a, then reduce fractions • In your factors, any remaining denominator gets moved in front of the x ac r s b

  16. Example 4

  17. You-Try #4

  18. Let A and B be real numbers, variables, or algebraic expressions, 1. A2 + 2AB + B2 = (A + B)2 2. A2 – 2AB + B2 = (A – B)2 If the first and third terms are both perfect squares, see if the middle term is two times the product of their square roots. Factoring Perfect Square Trinomials

  19. Example 5 • Factor: 16x2 – 56x + 49

  20. You-Try #5 • Factor: x2 + 14x + 49

  21. Difference of Two Perfect Squares

  22. Type Example A3 + B3= (A + B)(A2 – AB + B2) x3 + 8 = x3 + 23 = (x + 2)( x2 – x·2 + 22) = (x + 2)( x2 – 2x + 4) A3 – B3= (A – B)(A2 + AB + B2) 64x3 – 125 = (4x)3 – 53 = (4x – 5)((4x)2 + (4x)(5) + 52) = (4x – 5)(16x2 + 20x + 25) Sum and Difference of Two Perfect Cubes

  23. Example 6

  24. You-Try #6

  25. A Strategy for Factoring a Polynomial • If there is a common factor, factor out the GCF. • Count the number of terms in the polynomial and try factoring as follows: • If there are two terms, can the binomial be factored by one of the special forms including difference of two squares, sum of two cubes, or difference of two cubes? • If there are three terms, is the trinomial a perfect square trinomial? If the trinomial is not a perfect square trinomial, try factoring using the big X. • If there are four or more terms, try factoring by grouping. • Check to see if any factors with more than one term in the factored polynomial can be factored further. If so, factor completely.

  26. Factoring Flowchart Factor out GCF Count number of terms 4 2 • Check for: • Difference of perfect squares • Sum of perfect cubes • Difference of perfect cubes Factor by Grouping 3 Check for perfect square trinomial Use big X factoring Check each factor to see if it can be factored further

  27. Simplifying Rational Expressions • A rational expression is a fraction of two polynomials. • Factor each polynomial. • Cancel common factors.

  28. Example 7 • Simplify

  29. You-Try #7 • Simplify

  30. Assignment • Page 242 #15-39 odd, 43-49 all

  31. Warm-Up: November 14, 2011 • Simplify the following: • Show Mr. Szwast a correct warm-up to receive today’s worksheet. • If you have homework questions, ask during class or after school in room 709.

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