Section 6-12
Solving Equations Using Factoring
The zero product property says that if ab = 0, then
either a = 0 or b = 0.
So, if we have a quadratic equation broken into linear factors (ax + b)(cx + d),
we can reduce the problem to solving two linear equations.
Example:
Solve.
(x – 3)(2x + 8) = 0
By the zero product property, either
x – 3 = 0
or
2x + 8 = 0.
Solving both equations, we get the two solutions 3 and –4.