1. Factoring to Solve Quadratic Equations
ALGEBRA 1 LESSON 10-5
(For help, go to Lessons 2-2 and 9-6.)
Solve and check each equation.
n = – 9 = q + 16 = –3
Factor each expression.
4. 2c2 + 29c p2 + 32p x2 – 21x – 18 a 8
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2. Factoring to Solve Quadratic Equations
ALGEBRA 1 LESSON 10-5
Solutions
n = 2
4n = –4
n = –1
Check: 6 + 4(–1) = 6 + (–4) = 2
2. – 9 = 4
= 13
a = 104
Check: – 9 = 13 – 9 = 4
3. 7q + 16 = –3
7q = –19
q = –2
Check: 7 (–2 ) + 16 = 7(– ) + 16 = – = –3 a 8 a 8
104 8 5 7 5 7 19 7
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3. Factoring to Solve Quadratic Equations
ALGEBRA 1 LESSON 10-5
Solutions (continued)
4. 2c2 + 29c + 14 = (2c + 1)(c + 14)
Check: (2c + 1)(c + 14) = 2c2 + 28c + c + 14 = 2c2 + 29c + 14
5. 3p2 + 32p + 20 = (3p + 2)(p + 10)
Check: (3p + 2)(p + 10) = 3p2 + 30p + 2p + 20 = 3p2 + 32p + 20
6. 4x2 – 21x – 18 = (4x + 3)(x – 6)
Check: (4x + 3)(x – 6) = 4x2 – 24x + 3x – 18 = 4x2 – 21x – 18
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4. Factoring to Solve Quadratic Equations
ALGEBRA 1 LESSON 10-5
Solve (2x + 3)(x – 4) = 0 by using the Zero Product Property.
(2x + 3)(x – 4) = 0
2x + 3 = or x – 4 = 0
Use the Zero-Product Property.
2x = –3
Solve for x.
x = – 3 2 or
x = 4
Check: Substitute – for x. 3 2
Substitute 4 for x.
(2x + 3)(x – 4) = 0
[2(– ) + 3](– – 4) 0
[2(4) + 3](4 – 4) 0
(0)(– 5 ) = 0 1
(11)(0) = 0
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5. Factoring to Solve Quadratic Equations
ALGEBRA 1 LESSON 10-5
Solve x2 + x – 42 = 0 by factoring.
x2 + x – 42 = 0
(x + 7)(x – 6) = 0
Factor using x2 + x – 42
x + 7 = 0 or x – 6 = 0
Use the Zero-Product Property.
x = –7 or x = 6
Solve for x.
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6. Factoring to Solve Quadratic Equations
ALGEBRA 1 LESSON 10-5
Solve 3x2 – 2x = 21 by factoring.
3x2 – 2x = 21
Subtract 21 from each side.
(3x + 7)(x – 3) = 0
Factor 3x2 – 2x – 21.
3x + 7 = 0 or x – 3 = 0
Use the Zero-Product Property
3x = –7
Solve for x.
x = – or x = 3 7 3
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7. Factoring to Solve Quadratic Equations
ALGEBRA 1 LESSON 10-5
1. Solve (2x – 3)(x + 2) = 0.
Solve by factoring.
2. 6 = a2 – 5a 3. 12x + 4 = –9x2 4. 4y2 = 25
–2, 3 2 – 2 3 5 2
–1, 6
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