1. Solve Polynomial Equations in Factored Form March 25, 2014 Pages 575-579

2. 1. Solve (x – 4)(x + 2) = 0. (x – 4)(x + 2) = 0 Write original equation. x – 4 = 0 x = 4 Zero-product property Solve for x. ANSWER The solutions of the equation are 4 and –2. or x + 2 = 0 x = – 2

3. 2. Solve the equation (x – 5)(x – 1) = 0. (x – 5)(x – 1) = 0 Write original equation. x – 5 = 0 x = 5 Zero-product property Solve for x. ANSWER The solutions of the equation are 5 and 1. or x – 1 = 0 x = 1

4. SOLUTION Factor out the greatest common monomial factor. 3. 12x + 42y The GCF of 12 and 42 is 6. The variables x and y have no common factor. So, the greatest common monomial factor of the terms is 6. ANSWER 12x + 42y = 6(2x + 7y)

5. The GCF of 4 and 24 is 4. The GCF of x 4 and x 3 is x 3. So, the greatest common monomial factor of the terms is 4x 3. ANSWER 4x 4 + 24x 3 = 4x 3 (x + 6) SOLUTION Factor out the greatest common monomial factor. 4. 4x 4 + 24x 3

6. 5. Factor out the greatest common monomial factor from 14m + 35n. The GCF of 14 and 35 is 7. The variables m and n have no common factor. So, the greatest common monomial factor of the terms is 7. SOLUTION ANSWER 14m + 35n = 7(2m + 5n)

7. 6. Solve 2x 2 + 8x = 0. 2x 2 + 8x = 0. 2x(x + 4) = 0 2x = 0 x = 0 or x + 4 = 0 or x = – 4 ANSWER The solutions of the equation are 0 and – 4. Solve for x. Zero-product property Factor left side. Write original equation.

8. 7. Solve 6n 2 = 15n. 6n 2 – 15n = 0 3n(2n – 5) = 0 3n = 0 n = 0 2n – 5 = 0 n = 5 2 or Solve for n. Zero-product property Factor left side. Subtract 15n from each side. ANSWER The solutions of the equation are 0 and 5 2.

9. Solve the equation. a 2 + 5a = 0 a(a + 5) = 0 a = 0 or a + 5 = 0 or a = – 5 ANSWER The solutions of the equation are 0 and – 5. Solve for x. Zero-product property Factor left side. Write original equation. 8. a 2 + 5a = 0.

10. 3s 2 – 9s = 0 3s(s – 3) = 0 3s = 0 s= 0 or s – 3 = 0 or s = 3 ANSWER The solutions of the equation are 0 and 3. Solve for x. Zero-product property Factor left side. Write original equation. 9. 3s 2 – 9s = 0.

11. 10. 4x 2 = 2x. 4x 2 – 2x = 0 2x(2x – 1) = 0 2x = 0 x = 0 2x – 1 = 0 x = 1 2 or Solve for x. Zero-product property Factor left side. Subtract 2x from each side. ANSWER The solutions of the equation are 0 and 1 2. 4x 2 = 2x Write original equation.

12. HOMEWORK Page 578, #4-14, even, #18-24, even, #28-32, even