Download Lesson 8.3

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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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
1 and 15
3 and 5
Sum of Factors
16
8
x2 + 8x + 15 = (x + 3)(x + 5).
Check: x2 + 8x + 15
(x + 3)(x + 5)
= x2 + 5x + 3x + 15
= x2 + 8x + 15
9-5
Quick Check
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
–1 and –20
–2 and –10
–4 and –5
Sum of Factors
–21
–12
–9
c2 – 9c + 20 = (c – 5)(c – 4)
Quick Check
9-5
Factoring Trinomials of the Type x2 + bx + c
ALGEBRA 1 LESSON 9-5
Quick Check
a. Factor x2 + 13x – 48.
b. Factor n2 – 5n – 24.
Identify the pair of factors of –48
that has a sum of 13.
Factors of –48
1 and –48
48 and
–1
2 and –24
24 and
–2
3 and –16
16 and
–3
Identify the pair of factors of –24 that
has a sum of –5.
Sum of Factors
–47
47
–22
22
–13
13
Factors of –24
1 and –24
24 and –1
2 and –12
12 and –2
3 and –8
x2 + 13x – 48 = (x + 16)(x – 3)
Sum of Factors
–23
23
–10
10
–5
n2 – 5n – 24 = (n + 3)(n – 8)
9-5
Factoring Trinomials of the Type x2 + bx + c
ALGEBRA 1 LESSON 9-5
Factor d2 + 17dg – 60g2.
Find the factors of –60.
Identify the pair that has a sum of 17.
Factors of –60
1 and –60
60 and
–1
2 and –30
30 and
–2
3 and –20
20 and
–3
Sum of Factors
–59
59
–28
28
–17
17
d2 + 17dg – 60g2 = (d – 3g)(d + 20g)
9-5
Quick Check
Factoring Trinomials of the Type x2 + bx + c
ALGEBRA 1 LESSON 9-5
Factor each expression.
1. c2 + 6c + 9
(c + 3)(c + 3)
4. y2 + y – 110
(y + 11)(y – 10)
2. x2 – 11x + 18
(x – 2)(x – 9)
5. m2 – 2mn + n2
(m – n)(m – n)
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3. g2 – 2g – 24
(g – 6)(g + 4)