1. Factoring Trinomials of the Type ax2 + bx + c
ALGEBRA 1 LESSON 7-6
Factor 20x2 + 17x + 3.
20x2 + 17x + 3
F O I L
1 • 20 1 • • 20 = 23 1 • 3
1 • • 20 = 61 3 • 1
factors of a
factors of c
2 • 10 2 • • 10 = 16 1 • 3
2 • • 10 = 32 3 • 1
4 • 5 4 • • 5 = 17 1 • 3
20x2 + 17x + 3 = (4x + 1)(5x + 3)
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2. Factoring Trinomials of the Type ax2 + bx + c
ALGEBRA 1 LESSON 7-6
Factor 3n2 – 7n – 6.
3n2 –7n –6
(1)(3)     (1)(–6) + (1)(3) = –3 (1)(–6)
(1)(1) + (–6)(3) = –17 (–6)(1)
(1)(–3) + (2)(3) = 3 (2)(–3)
(1)(2) + (–3)(3) = –7 (–3)(2)
3n2 – 7n – 6 = (n – 3)(3n + 2)
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3. Factoring Trinomials of the Type ax2 + bx + c
ALGEBRA 1 LESSON 7-6
Factor 18x2 + 33x – 30 completely.
18x2 + 33x – 30 = 3(6x2 + 11x – 10) Factor out the GCF.
Factor 6x2 + 11x – 10.
6x2 + 11x –10
(2)(3) (2)(–10) + (1)(3) = –17 (1)(–10)
(2)(1) + (–10)(3) = –28 (–10)(1)
(2)(–5) + (2)(3) = –4 (2)(–5)
(2)(2) + (–5)(3) = –11 (–5)(2)
(2)(–2) + (5)(3) = 11 (5)(–2)
6x2 + 11x – 10 = (2x + 5)(3x – 2)
18x2 + 33x – 30 = 3(2x + 5)(3x – 2)
Include the GCF in your final answer.
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4. Step 1: 24h2 + 10h – 6 = 2(12h2 + 5h – 3) Factor out the GCF, 2.
Factoring by Grouping
ALGEBRA 1 LESSON 7-6
Factor 24h2 + 10h – 6.
Step 1: 24h2 + 10h – 6 = 2(12h2 + 5h – 3)   Factor out the GCF, 2.
Step 2: 12 • –3 = –36 Find the product ac.
Step 3: Factors Sum
–2(18) = –36 – = 16
–3(12) = –36 – = 9
–4(9) = –36 –4 + 9 = 5
Find two factors of ac that have a sum b. Use mental math to determine a good place to start.
Step 4:  12h2 – 4h + 9h – 3 Rewrite the trinomial.
Step 5:   4h(3h – 1) + 3(3h – 1) Factor by grouping.
  (4h + 3)(3h – 1) Factor again.
24h2 + 10h – 6 = 2(4h + 3)(3h – 1) Include the GCF in your final answer.
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5. Step 1: 3x(12x2 + 17x + 6) Factor out the GCF, 3x.
Factoring by Grouping
ALGEBRA 1 LESSON 7-6
A rectangular prism has a volume of 36x3 + 51x2 + 18x. Factor to find the possible expressions for the length, width, and height of the prism.
Factor 36x3 + 51x2 + 18x.
Step 1: 3x(12x2 + 17x + 6) Factor out the GCF, 3x.
Step 2: 12 • 6 = 72 Find the product ac.
Step 3:  Factors     Sum
4 • = 22
6 • = 18
8 • = 17
Find two factors of ac that have sum b. Use mental math to determine a good place to start.
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6. Step 4: 3x(12x2 + 8x + 9x + 6) Rewrite the trinomial.
Factoring by Grouping
ALGEBRA 1 LESSON 7-6
(continued)
Step 4: 3x(12x2 + 8x + 9x + 6) Rewrite the trinomial.
Step 5: 3x[4x(3x + 2) + 3(3x + 2)] Factor by grouping.
3x(4x + 3)(3x + 2) Factor again.
The possible dimensions of the prism are 3x, (4x + 3), and (3x + 2).
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7. Factoring Trinomials of the Type ax2 + bx + c
ALGEBRA 1 LESSON 7-6
Factor each expression.
1. 3x2 – 14x + 11
2. 6t2 + 13t – 63
3. 9y2 – 48y – 36
(x – 1)(3x – 11)
(2t + 9)(3t – 7)
3(3y + 2)(y – 6)
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