Solving Equations by Factoring
Definition: Any equation that can be put in the form ax2 + bx + c = 0 where a, b, and
c are real numbers (a ≠ 0), is called a quadratic equation. The
standard form for a
quadratic equation:
ax2 + bx + c = 0
Zero-Factor Theorem: For real numbers A and B, if A·B = 0 then A = 0 or B = 0, or both.
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WHAT TO DO: |
HOW TO DO IT: |
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1. Solve the equation x 2 − 5x − 6 = 0
Scratch: Find a numbers whose product is 6
with difference of 5 , larger sign “−â€.
Set each factor equal to zero:
The solution:
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x
2 − 5x − 6 = 0
(x − 6)(x + 1) = 0
(x − 6) = 0 or (x + 1) = 0
x = 6 or x = − 1
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| Check the equation x 2
− 5x − 6 = 0 |
(6)2 − 5(6) − 6 = 0 , (-1)2 − 5(-1) − 6 = 0 |
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2. Solve the equation x 2 = 7x − 12
Rewrite as a standard equation:
Scratch: Find a pair of numbers whose
product is 12 with sum of 7.
Set each factor equal to zero:
The solution:
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x 2 = 7x − 12 x
2 − 7x + 12 = 0
(x − 4)(x − 3) = 0
(x − 4) = 0 or (x − 3) = 0
x = 4 or x = 3
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| Check the equation x 2
= 7x − 12 |
(4)2
= 7(4) − 12 , (3)2 = 7(3) − 12 |
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2. Solve the equation x 2 = 12x
Rewrite as a standard equation:
Set each factor equal to zero:
The solution:
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x
2 = 12x
x 2 − 12x = 0
x·(x − 12) = 0
x = 0 or (x − 12) = 0
x = 0 or x = 12 |
| Check the equation x 2 = 12x
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(0)2 = 12(0) , (12)2 = 12(12) |
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