Transcript Factoring Trinomials of the Type x2 + bx + c

Factoring Trinomials of the Type
2 + bx + c
ax
Find the greatest common factor.
ALGEBRA 1 LESSON 9-6
(For help, go to Lessons 9-2 and 9-5.)
1. 12x2 + 6x
2. 28m2 – 35m + 14
3. 4v3 + 36v2 + 10
Factor each expression.
4. x2 + 5x + 4
5. y2 – 3y – 28
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6. t2 – 11t + 30
Factoring Trinomials of the Type
ax2 + bx + c
Solutions
ALGEBRA 1 LESSON 9-6
1. 12x2 + 6x
12x2 = 2 • 2 • 3 • x • x; 6x = 2 • 3 • x;
GCF = 2 • 3 • x = 6x
2. 28m2 – 35m + 14
28m2 = 2 • 2 • 7 • m • m; 35m = 5 • 7 • m; 14 = 2 • 7;
GCF = 7
3. 4v3 + 36v2 + 10
4v3 = 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 + 4)(y – 7)
6. Factors of 30 with a sum of –11: –5 and –6
t2 – 11t + 30 = (t – 5)(t – 6)
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Factoring Trinomials of the Type
2 + bx + c
ax
Factor 20x + 17x + 3.
ALGEBRA 1 LESSON 9-6
2
20x2
F
factors
of a
O
+ 17x
+3
I
L
1 • 20
1 • 3 + 1 • 20 = 23
1 • 1 + 3 • 20 = 61
1•3
3•1
2 • 10
2 • 3 + 1 • 10 = 16
2 • 1 + 3 • 10 = 32
1•3
3•1
4•5
4 • 3 + 1 • 5 = 17
1•3
20x2 + 17x + 3 = (4x + 1)(5x + 3)
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factors
of c
Factoring Trinomials of the Type
2 + bx + c
ax
Factor 3n – 7n – 6.
ALGEBRA 1 LESSON 9-6
2
3n2
(1)(3)
–7n
–6
(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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Factoring Trinomials of the Type
2 + bx + c
ax
Factor 18x + 33x – 30 completely.
ALGEBRA 1 LESSON 9-6
2
18x2 + 33x – 30 = 3(6x2 + 11x – 10)
Factor out the GCF.
Factor 6x2 + 11x – 10.
6x2
(2)(3)
+ 11x
(2)(–10) + (1)(3) = –17
(2)(1) + (–10)(3) = –28
(2)(–5) + (2)(3) = –4
(2)(2) + (–5)(3) = –11
(2)(–2) + (5)(3) = 11
–10
(1)(–10)
(–10)(1)
(2)(–5)
(–5)(2)
(5)(–2)
6x2 + 11x – 10 = (2x + 5)(3x – 2)
18x2 + 33x – 30 = 3(2x + 5)(3x – 2)
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Include the GCF in your final answer.
Factoring Trinomials of the Type
2 + bx + c
ax
Factor each expression.
ALGEBRA 1 LESSON 9-6
1. 3x2 – 14x + 11
(x – 1)(3x – 11)
2. 6t2 + 13t – 63
(2t + 9)(3t – 7)
3. 9y2 – 48y – 36
3(3y + 2)(y – 6)
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