Factoring Trinomials of the Type x2 + bx + c ALGEBRA 1 LESSON 7-5 Factor x2 + 8x + 15. Find the factors of 15. Identify the pair that has a sum of 8. Factors of 15 Sum of Factors 1 and 15 16 3 and 5 8 x2 + 8x + 15 = (x + 3)(x + 5). = x2 + 5x + 3x + 15 Check: x2 + 8x + 15 (x + 3)(x + 5) = x2 + 8x + 15 7-5

Factoring Trinomials of the Type x2 + bx + c ALGEBRA 1 LESSON 7-5 Factor c2 – 9c + 20. Since the middle term is negative, find the negative factors of 20. Identify the pair that has a sum of –9. Factors of 20 Sum of Factors –1 and –20 –21 –2 and –10 –12 –4 and –5 –9 c2 – 9c + 20 = (c – 5)(c – 4) 7-5

Factoring Trinomials of the Type x2 + bx + c ALGEBRA 1 LESSON 7-5 a. Factor x2 + 13x – 48. b. Factor n2 – 5n – 24. Identify the pair of factors of –48 that has a sum of 13. Identify the pair of factors of –24 that has a sum of –5. Factors of –48 Sum 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 16 Factors of –24 Sum of Factors 1 and –24 –23 24 and –1 23 2 and –12 –10 12 and –2 10 3 and –8 –5 x2 + 13x – 48 = (x + 16)(x – 3) n2 – 5n – 24 = (n + 3)(n – 8) 7-5

Factoring Trinomials of the Type x2 + bx + c ALGEBRA 1 LESSON 7-5 Factor d2 + 17dg – 60g2. Factors of –60 Sum 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. d2 + 17dg – 60g2 = (d – 3g)(d + 20g) 7-5

Factoring Trinomials of the Type x2 + bx + c ALGEBRA 1 LESSON 7-5 Factor each expression. 1. c2 + 6c + 9 2. x2 – 11x + 18 3. g2 – 2g – 24 4. y2 + y – 110 5. m2 – 2mn + n2 (c + 3)(c + 3) (x – 2)(x – 9) (g – 6)(g + 4) (y + 11)(y – 10) (m – n)(m – n) 7-5