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Solving Quadratic Equations – Factoring Method
• A Quadratic Equation is an equation that can be
written in the form
ax2  bx  c  0
a, b, and c are real numbers, a  0
Solving quadratic equations by the factoring method
is very similar to solving polynomial equations by
factoring, which was discussed at length in an earlier
chapter.
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Factoring Method to Solve Quadratic Equations
1. Move all non-zero terms to one side of the
equation and simplify.
2. Factor the quadratic expression.
3. Set each factor containing a variable equal to zero.
The Principle of Zero Products is used for this step
4. Solve the resulting equations.
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• Example 1:
x  x  12
2
Solve the equation
x  x  12  0
( x  4)( x  3)  0
2
Move all terms to left side
Factor
Set each factor to zero
x4  0
x3 0
x  4, 3
Solve each equation.
x  3, 4
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• Example 2:
10  7 x  12 x
Solve the equation
Move all terms to right side
since the quadratic term is
positive on that side
Factor
Set each factor to zero
2
0  12 x  7 x  10
2
0  (3x  2)(4 x  5)
3x  2  0
4x  5  0
2 5
x  ,
3 4
Solve each equation.
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• Example 3:
5 x  20
2
Solve the equation
5 x  20  0
2
Move all terms to left side
5( x2  4)  0
5( x  2)( x  2)  0
Factor
Set each variable factor to
zero
x2  0
x20
x  2
Solve each equation.
Table of Contents
Table of Contents