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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.