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.

I. Factoring Quadratic Expressions

Example 1 c and d

c. 27a2 – 18a

d. 5x(2x + 1) – 2(2x + 1)

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)

Example 1 – Factor by Trial & Error

Example 1b

Example 1 c and d

c. x2 + 9x + 20

Example 2 – Factor and check by graphing

Example 2b

3x2 +11x – 20Guess and Check

Factoring the Difference of 2 SquaresFactoring Perfect Square Trinomials

a2 – b2 = (a + b)(a – b) a2 + 2ab + b2 = (a + b)2 or a2 – 2ab + b2 = (a – b)2

c. 9x4 – 49 d. 9x2 – 36x + 36

Zero Product Property

IV. A zero of a function f 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.

Example 1

Example 1 c and d

c. f(x) = 3x2 – 12x

d. g(x) = x2 + 4x – 21

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?

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.