Factoring Trinomials of the Type x2 + bx + c

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Factoring Trinomials of the Type x2 + bx + c ALGEBRA 1 LESSON 9-5 (For help, go to Skills Handbook page 721.) List all of the factors of each number. 1. 24 2. 12 3. 54 4. 15 5. 36 6. 56 7. 64 8. 96 5-7

Factoring Trinomials of the Type x2 + bx + c ALGEBRA 1 LESSON 9-5 Solutions 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 5-7

Factoring Trinomials of the Type x2 + bx + c ALGEBRA 1 LESSON 9-5 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 5-7

Factoring Trinomials of the Type x2 + bx + c ALGEBRA 1 LESSON 9-5 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) 5-7

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