1. 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.
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2. 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
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3. Factoring Trinomials of the Type x2 + bx + c
ALGEBRA 1 LESSON 9-5
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 –
2 and –24 –22
24 and –
3 and –16 –13
16 and –
Factors of –24 Sum of Factors
1 and –24 –23
24 and –
2 and –12 –10
12 and –
3 and –8 –5
x2 + 13x – 48 = (x + 16)(x – 3)
n2 – 5n – 24 = (n + 3)(n – 8)
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4. Factoring Trinomials of the Type x2 + bx + c
ALGEBRA 1 LESSON 9-5
Factor d2 + 17dg – 60g2.
Factors of –60 Sum of Factors
1 and –60 –59
60 and –
2 and –30 –28
30 and –
3 and –20 –17
20 and –
Find the factors of –60.
Identify the pair that has a sum of 17.
d2 + 17dg – 60g2 = (d – 3g)(d + 20g)
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5. Factoring Trinomials of the Type x2 + bx + c
ALGEBRA 1 LESSON 9-5
Factor each expression.
1. c2 + 6c x2 – 11x g2 – 2g – 24
4. y2 + y – m2 – 2mn + n2
(c + 3)(c + 3)
(x – 2)(x – 9)
(g – 6)(g + 4)
(y + 11)(y – 10)
(m – n)(m – n)
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