1. Factoring Trinomials of the Type ax2 + bx + c
ALGEBRA 1 LESSON 9-6
(For help, go to Lessons 9-2 and 9-5.)
Find the greatest common factor.
1. 12x2 + 6x 2. 28m2 – 35m v3 + 36v2 + 10
Factor each expression.
4. x2 + 5x y2 – 3y – t2 – 11t + 30
Check Skills You’ll Need
9-6

2. Factoring Trinomials of the Type ax2 + bx + c
ALGEBRA 1 LESSON 9-6
Solutions
1. 12x2 + 6x 12x2 = 2 • 2 • 3 • x • x; 6x = 2 • 3 • x; GCF = 2 • 3 • x = 6x
2. 28m2 – 35m m2 = 2 • 2 • 7 • m • m; 35m = 5 • 7 • m; 14 = 2 • 7; GCF = 7
3. 4v3 + 36v v3 = 2 • 2 • v • v • v; 36v2 = 2 • 2 • 3 • 3 • v • v; 10 = 2 • 5; GCF = 2
4. Factors of 4 with a sum of 5: 1 and 4 x2 + 5x + 4 = (x + 1)(x + 4)
5. Factors of –28 with a sum of –3: 4 and –7 y2 – 3y – 28 = (y – 7)(y + 4)
6. Factors of 30 with a sum of –11: –5 and –6 t2 – 11t + 30 = (t – 5)(t – 6)
9-6

3. Factoring Trinomials of the Type ax2 + bx + c
ALGEBRA 1 LESSON 9-6
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)
Quick Check
9-6

4. Factoring Trinomials of the Type ax2 + bx + c
ALGEBRA 1 LESSON 9-6
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)
Quick Check
9-6

5. Factoring Trinomials of the Type ax2 + bx + c
ALGEBRA 1 LESSON 9-6
Quick Check
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.
9-6

6. Factoring Trinomials of the Type ax2 + bx + c
ALGEBRA 1 LESSON 9-6
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)
9-6

7. Factoring Special Cases
ALGEBRA 1 LESSON 9-7
(For help, go to Lessons 8–4 and 9-4.)
Simplify each expression.
1. (3x)2 2. (5y)2 3. (15h2)2 4. (2ab2)2
Simplify each product.
5. (c – 6)(c + 6) 6. (p – 11)(p – 11) 7. (4d + 7)(4d + 7)
Check Skills You’ll Need
9-7