Section 5.3 Factoring Quadratic Expressions

1. Section 5.3Factoring Quadratic Expressions Objectives: Factor a quadratic expression. Use factoring to solve a quadratic equation and find the zeros of a quadratic function. Standard: 2.8.11.N. Solve quadratic equations.

2. I. Factoring Quadratic Expressions

3. Example 1 c and d c. 27a2 – 18a d. 5x(2x + 1) – 2(2x + 1)

4. II. Factoring x2+ bx + c. (TRIAL & ERROR) • To factor an expression of the form ax2+ bx + c where a = 1, look for integers r and s such that r • s = c and r + s = b. Then factor the expression. • x2 + bx + c = (x + r)(x + s)

5. Example 1 – Factor by Trial & Error

6. Example 1b

7. Example 1 c and d c. x2 + 9x + 20

8. Example 2 – Factor and check by graphing

9. Example 2b 3x2 +11x – 20 Guess and Check

10. Factoring the Difference of 2 SquaresFactoring Perfect Square Trinomials • a2 – b2 = (a + b)(a – b) • a2 + 2ab + b2 = (a + b)2 ora2 – 2ab + b2 = (a – b)2 • 9x4 – 49 • 9x2 – 36x + 36

11. Zero Product Property • IV. A zero of a functionf is any number r such that f(r) = 0. Zero-Product Property • If pq = 0, then p = 0 or q = 0. • An equation in the form of ax2+ bx + c = 0 is called the general form of a quadratic equation.

12. Example 1

13. Example 1 c and d c. f(x) = 3x2 – 12x d. g(x) = x2 + 4x – 21

14. Ex 2. • An architect created a proposal for the fountain at right. Each level (except the top one) is an X formed by cubes. The number of cubes in each of the four parts of the X is one less than the number on the level below. A formula for the total number of cubes, c, in the fountain is given by c = 2n - n, where n is the number of levels in the fountain. How many levels would a fountain consisting of 66 cubes have?

15. Writing Activities 2. a. Shannon factored 4x2 – 36x + 81 as (2x + 9)2. Was she correct? Explain. b. Brandon factored 16x2 – 25 as (4x – 5)2. Was he correct? Explain.