1. Solving equations by factoring
Section 6.4
Solving equations by factoring

2. The Zero-Factor Theorem
If a and b are real numbers and
(a)(b) = 0, then
either a = 0 or b = 0

3. 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.

4. EX: Solve
x2 – 128 = 0
m2 + 1 = -7m
x(x2 – 3x) = 2x(4x – 8) – 9x
4. 4x(x + 7) = -49

5. 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.