2. 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.

3. I. Factoring Quadratic Expressions
To factor an expression containing two or more terms, factor out the greatest common factor (GCF) of the two expressions.
Factor each quadratic expression.
1. 3a2 – 12a
2. 3x(4x + 5) – 5(4x + 5)

4. Examples
3. 27a2 – 18a
4. 5x(2x + 1) – 2(2x + 1)

5. II. Factoring x2+ bx + c.
To factor an expression of the form ax2+ bx + c where a = 1
Find two numbers that
add to equal
And multiply to equal 5 6 8 7
-26 48 -9
-36

6. Example 1 – Factor by Trial & Error
Factor x2 + 5x + 6.

7. Example 1b
Factor x2 – 7x – 30.

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

9. 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

10. Example 2 – Factor and check by graphing
Factor 6x2 + 11x Check by graphing.

11. Example 2b
Factor 3x2 +11x – 20. Check by graphing.

12. 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

13. 1. 3x2 + 18
4. x2 – 10x - 24
5. x2 + 4x - 32
2. x – 4x2
6. 3x2 + 7x + 2
3. x2 + 8x + 16
7. 3x2 – 5x - 2

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

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

16. Zero-Product Property
A zero of a function f is any number r such that f(r) = 0.
Zero-Product Property
When multiplying two numbers 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.

17. Example 1

18. Example 1 c and d c. f(x) = 3x2 – 12x d. g(x) = x2 + 4x - 21
Use the zero product property to find the zeros of each function.
c. f(x) = 3x2 – 12x
d. g(x) = x2 + 4x - 21

19. Pg. 296 #59, 61, 63
1. 3x2 – 5x = 2
2. 6x2 – 17x = -12
3. 3x2 + 3 = 10

20. 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.

22. Homework
Integrated Algebra II- Section 5.3 Level A
Academic Algebra II- Section 5.3 Level B