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5.3 More on Factoring Trinomials

5.3 More on Factoring Trinomials. More on Factoring Trinomials. Trinomials such as 2 x 2 + 7 x + 6, in which the coefficient of the squared term is not 1, are factored with extensions of the methods from the previous sections. Slide 5.3-3. Objective 1 .

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5.3 More on Factoring Trinomials

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  1. 5.3 More on Factoring Trinomials

  2. More on Factoring Trinomials Trinomials such as 2x2 + 7x + 6, in which the coefficient of the squared term is not 1, are factored with extensions of the methods from the previous sections. Slide 5.3-3

  3. Objective 1 Factor trinomials by grouping when the coefficient of the second-degree term is not 1. Slide 5.3-4

  4. Sum Product is 2 · 6 = 12 Factor trinomials by grouping when the coefficient of the second-degree term is not 1. Recall that a trinomial such as m2 + 3m + 2 is factored by finding two numbers whose product is 2 and whose sum is 3. To factor 2x2 + 7x + 6, we look for two integers whose product is 2·6 = 12 and whose sum is 7. Slide 5.3-5

  5. Factor trinomials by grouping when the coefficient of the second-degree term is not 1. (cont’d) By considering pairs of positive integers whose product is 12, we find the necessary integers to be 3 and 4. We use these integers to write the middle term, 7x, as 7x = 3x + 4x. The trinomial 2x2 + 7x + 6 becomes Slide 5.3-6

  6. CLASSROOM EXAMPLE 1 Factoring Trinomials by Grouping Solution: Factor. Slide 5.3-7

  7. CLASSROOM EXAMPLE 2 Factoring a Trinomial with a Common Factor by Grouping Solution: Factor 6p4 + 21p3 + 9p2. Slide 5.3-8

  8. Objective 2 Factor trinomials by using the FOIL method. Slide 5.3-9

  9. Factor trinomials by using the FOIL method. (cont’d) There is an alternative method of factoring that uses trial and error. To factor 2x2 + 7x + 6 by trial and error, we use the FOIL method in reverse, trying to find two binomials whose products work. Incorrect Incorrect Correct If the terms of the original polynomial have greatest common factor 1, then all of that polynomials binomial factors also have GCF 1. Slide 5.3-10

  10. CLASSROOM EXAMPLE 3 Factoring a Trinomial with All Positive Terms by Using FOIL Solution: Factor 6p2 + 19p + 10. Slide 5.3-11

  11. CLASSROOM EXAMPLE 4 Factoring a Trinomial with a Negative Middle Term by Using FOIL Solution: Factor 10m2– 23m + 12. Slide 5.3-12

  12. CLASSROOM EXAMPLE 5 Factoring a Trinomial with a Negative Constant Term by Using FOIL Solution: Factor 5p2 + 13p– 6. Slide 5.3-13

  13. CLASSROOM EXAMPLE 6 Factoring a Trinomial with Two Variables Solution: Factor 6m2 + 11mn– 10n2. Slide 5.3-14

  14. CLASSROOM EXAMPLE 7 Factoring Trinomials with Common Factors Factor. Solution: Slide 5.3-15

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