Section 6.4
SOLVING EQUATIONS
BY FACTORING
The Zero-Factor Theorem
If a and b are real numbers and

(a)(b) = 0, then
 either a = 0 or b = 0

To Solve:
Rearrange (if needed) so the
polynomial is in standard form:
ax2 + bx + c = 0
 Factor… (____) (____) = 0
 Set each (Factor) = 0

◦ Note: Only factors that contain a
variable are set equal to zero…
saying 3 = 0 makes little sense!

Solve each equation.
EX: Solve

1.
2x2 – 128 = 0

2.
6m2 + 1 = -7m

3.
4x(x2 – 3x) = 2x(4x – 8) – 9x

4. 4x(x + 7) = -49
The Pythagorean Theorem

For any right triangle (sides A and B,
hypotenuse C),
 A2
+ B2 = C2
Ex 1. If the height of a right triangle is x,
base is 8, hypotenuse is (x + 4)… find x.
Then give the length of all three sides.
Ex 2. The 2 sides are n and (2n – 1) and the
hypotenuse is (2n + 1)… find n. Then give
the length of all three sides.