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 or a2 2ab b2
  (a b)2

• 9x4 49

• 9x2 36x 36

11
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.

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.