1. Factoring Trinomials of the Type x 2 + bx + c ALGEBRA 1 LESSON 9-5 1.Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 2.Factors of 12: 1, 2, 3, 4, 6, 12 3.Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54 4.Factors of 15: 1, 3, 5, 15 5.Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 6.Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56 7.Factors of 64: 1, 2, 4, 8, 16, 32, 64 8.Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 Solutions 9-5

2. Factoring Trinomials of the Type x 2 + bx + c ALGEBRA 1 LESSON 9-5 Factor x 2 + 8x + 15. Find the factors of 15. Identify the pair that has a sum of 8. Factors of 15Sum of Factors 1 and 1516 3 and 5 8 x 2 + 8x + 15 = (x + 3)(x + 5). = x 2 + 5x + 3x + 15 Check: x 2 + 8x + 15 (x + 3)(x + 5) = x 2 + 8x + 15 Quick Check 9-5

3. Factoring Trinomials of the Type x 2 + bx + c ALGEBRA 1 LESSON 9-5 Factor c 2 – 9c + 20. Since the middle term is negative, find the negative factors of 20. Identify the pair that has a sum of –9. c 2 – 9c + 20 = (c – 5)(c – 4) Factors of 20Sum of Factors –1 and –20–21 –2 and –10–12 –4 and –5–9 9-5 Quick Check

4. Factoring Trinomials of the Type x 2 + bx + c ALGEBRA 1 LESSON 9-5 a. Factor x 2 + 13x – 48. Identify the pair of factors of –48 that has a sum of 13. b. Factor n 2 – 5n – 24. Identify the pair of factors of –24 that has a sum of –5. x 2 + 13x – 48 = (x + 16)(x – 3) n 2 – 5n – 24 = (n + 3)(n – 8) Factors of –48Sum of Factors 1 and –48–47 48 and –1 47 2 and –24–22 24 and –2 22 3 and –16–13 16 and –3 13 Factors of –24Sum of Factors 1 and –24–23 24 and–1 23 2 and–12–10 12 and–2 10 3 and–8 –5 Quick Check 9-5

5. Factoring Trinomials of the Type x 2 + bx + c Factor d 2 + 17dg – 60g 2. ALGEBRA 1 LESSON 9-5 Factors of –60Sum of Factors 1 and –60–59 60 and –1 59 2 and –30–28 30 and –2 28 3 and –20–17 20 and –3 17 Find the factors of –60. Identify the pair that has a sum of 17. d 2 + 17dg – 60g 2 = (d – 3g)(d + 20g) Quick Check 9-5

6. Factoring Trinomials of the Type x 2 + bx + c Factor each expression. 1.c 2 + 6c + 92.x 2 – 11x + 183.g 2 – 2g – 24 4.y 2 + y – 1105.m 2 – 2mn + n 2 ALGEBRA 1 LESSON 9-5 (c + 3)(c + 3)(x – 2)(x – 9)(g – 6)(g + 4) (y + 11)(y – 10)(m – n)(m – n) 9-5