Section 6.5
Solving Equations by Factoring
Overview
• In this section we apply the factoring
strategies developed in the first four sections
to solving equations.
• It is strongly recommended that you review
carefully Sections 6.1 through 6.3 before
attempting the problems in this section.
The Zero Product Property
• If ab = 0 then either a = 0 or b = 0.
• English translation: If two “things” are
multiplied together and the product is 0, then
either one “thing” is 0 or the other “thing” is
0.
• We apply this property to solving equations.
Steps in the Process
1. Apply the distributive property and/or the
FOIL method if necessary.
2. Move all the terms to the left hand side of
the equation (set the equation equal to 0).
3. Combine all like terms and write the left
hand side in descending order.
4. Factor the left hand side.
5. Set each factor equal to 0 and solve.
Examples
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(x + 7)(x + 3) = 0
x2 + x – 12 = 0
2x2 = 3 – x
(3x + 1)(x – 3) = 2 + 3(x + 5)
-2x2 + 8 = 0
6x3 – 13x2 – 5x = 0
2x3 + x2 – 98x – 49 = 0