Transcript Factoring Trinomials of the Type x2 + bx + c

Factoring Trinomials of the Type
2 number.
bx + c
List all of the factors ofx
each +
ALGEBRA 1 LESSON 9-5
(For help, go to Skills Handbook page 721.)
1. 24
2. 12
3. 54
4. 15
5. 36
6. 56
7. 64
8. 96
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Factoring Trinomials of the Type
x2 + bx + c
Solutions
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
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Factoring Trinomials of the Type
2 + bx + c
x
Factor x + 8x + 15.
ALGEBRA 1 LESSON 9-5
2
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
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Factoring Trinomials of the Type
2 + bx + c
x
Factor c – 9c + 20.
ALGEBRA 1 LESSON 9-5
2
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)
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Factoring Trinomials of the Type
Factor each expression.
x2 + bx + c
ALGEBRA 1 LESSON 9-5
1. c2 + 6c + 9
(c + 3)(c + 3)
2. x2 – 11x + 18
(x – 2)(x – 9)
3. m2 – 2mn + n2
(m – n)(m – n)
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