1. Section 5.3 Factoring Quadratic Expressions
Objectives: Factor a quadratic expression.
Use factoring to solve a quadratic equation and find the zeros of a quadratic function.
Standard: 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. (Using Trial & Error)
To factor an expression of the form ax2+ bx + c where a = 1
Find two factors of c (which we will call j and k)
j • k = c and j + k = b.
Write the factor of the expression as
x2 + bx + c = (x + j)(x + k)

5. Example 1 – Factor by Trial & Error

6. Example 1b

7. Example 1 c and d
c. x2 + 9x + 20
d. x2 – 10x – 11

8. II. Factoring ax2+ bx + c. (Using Trial & Error)
To factor an expression of the form ax2+ bx + c where a > 1
Find all the factors of c
Find all the factors of a
Place the factors of a in the first position of each set of parentheses
Place the factors of c in the second position of each set of parentheses
Try combinations of factors so that when doing FOIL the Firsts mult to equal a; the Outer and Inners mult then add to equal b; the Lasts mult to equal c

9. Example 2 – Factor and check by graphing

10. Example 2b
3x2 +11x – 20

11. Example 2b 3x2 +11x – 20 Guess and Check
(3x + 1)(x – 20) (3x – 1)(x + 20) (3x + 20)(x – 1) (3x – 20)(x + 1)
-60x +1x ≠ 11x x – 1x ≠ 11x x + 20x ≠ 11x 3x – 20x ≠ 11x
(3x + 2)(x – 10) (3x – 2)(x + 10) (3x + 10)(x – 2) (3x – 10)(x + 2)
-30x + 2x ≠ 11x x – 2x ≠ 11x x +10x ≠ 11x x – 10x ≠ 11x
(3x + 4)(x – 5) (3x – 4)(x + 5) (3x + 5)(x – 4) (3x – 5)(x + 4)
-15x + 4x ≠ 11x x – 4x = 11x x + 5x ≠ 11x 12x – 5x ≠ 11x

12. Pg. 296 #31, 33, 41, 43, 45, 55, 57

13. Factoring the Difference of 2 Squares
a2 – b2 = (a + b)(a – b)
Factor the following expressions:
y2 - 25
9x4 - 49
x4 - 16

14. Factoring Perfect Square Trinomials
a2 + 2ab + b2 = (a + b)2 or a2 – 2ab + b2 = (a – b)2
Factor the following expressions:
4x2 – 24x + 36
This is a Perfect Square Trinomial because:
9x2 – 36x + 36

15. Zero-Product Property
A zero of a function f is any number r such that f(r) = 0.
Zero-Product Property
When multiplying two number p and q:
If p = 0 then p ● q = 0.
If q = 0 then p ● q = 0.
An equation in the form of ax2+ bx + c = 0 is called the general form of a quadratic equation. The solutions to this equation are called the zeros and are the locations where the parabola crosses the x-axis.

16. Example 1

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

18. Pg. 296 #59, 61, 63

19. 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.

20. Homework
Pg #30-92 even