1. 1 7.5 Factoring Trinomials CORD Math Mrs. Spitz Fall 2006

2. 2 of 14 Objectives Factor quadratic trinomials.

3. 3 of 14 Assignment Pg. 274 #5-43 all

4. 4 of 14 Introduction In Lesson 7.1, you learned that when two numbers are multiplied, each number is a factor of the product. Similarly, if two binomials are multiplied, each binomial is a factor of the product.

5. 5 of 14 Consider the binomials 5x + 2 and 3x + 7. You can use the FOIL method to find their products. The binomials 5x + 2 and 3x + 7 are factors of 15x 2 + 41x + 14.

6. 6 of 14 FOIL When using the FOIL method, look at the product of the coefficients of the first and last terms, 15 and 14. Notice that it is the same as the product of the two terms 35 and 6, whose sum is the coefficient of the middle term. You can use this pattern to factor quadratic trinomials, such as 2y 2 + 7y +6.

7. 7 of 14 Ex. 1: Factor 5x 2 - 17x + 14 The product of 5 and 14 is 70. Since the product is positive and the sum is negative, both factors must be negative. Possibilities: Factors of 70Sum of factors -1, -70-1+ -70 = -71 NOT -2, -35-2 + -35 = -37 NOT -5, -14-5 + -14 = -19 NOT -7, -10-7 + -10 = -17 YES

8. 8 of 14 Now what? Stop when you find the factors. Check using FOIL Factor GCF from each Factor by grouping

9. 9 of 14 Ex. 2: What does a factored trinomial look like? (x )(x ) Look at the trinomial. Are the signs positive, negative or both positive and negative. For example: x 2 + 5x - 6 -+ What are the factors of 6 that subtract to give you 5? 6 - 1 = 5 16 One sign is positive, one negative meaning you are looking for factors of 6 that subtract to give you 5—the number in the middle. With no coefficient (the number in front of the variable x 2 (the letter), it’s pretty easy to figure out.

10. 10 of 14 Ex. 3: Factor 2n 2 -11n + 7 You must find two numbers whose product is 2 ·7 or 14 and whose sum is -11. Factors of 14Sum of factors -1, -14-1+ -14 = -15 -2, -7-2 + -7 = -9 There are no factors of 14 whose sum is -11. Therefore this expression cannot be factored using integers. It is prime.

11. 11 of 14 Ex. 4: Factor 7a 2 + 22a + 3 You must find two numbers whose product is 7 · 3 or 21 and whose sum is -11. Factors of 21Sum of factors 1, 211 + 21 = 22 YES 3, 73 + 7 = 10 NO Factors of 21 that add to give you 22 are 1 and 22. Factored format is (7a+1)(a+3)

12. 12 of 14 Use FOIL to check your answer.

13. 13 of 14 Ex. 5: Factor 2q 2 – 9q - 18 You must find two numbers whose product is 2 · 18 or 36 and whose sum is -9. Factors of 36Sum of factors -36, 1-36+1=-35 NOT -18, 2-18 + 2 = -16 NOT -12, 3-12 + 3 = -9 YES Factors of -36 that add to give you -9 are -12 and 3. Factored format is (2q + 3)(q – 6)

14. 14 of 14 Use FOIL to check your answer.