1. Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities
Chapter 5 – Quadratic Functions and Inequalities
5.3 – Solving Quadratic Equations by Factoring

2. 5.3 – Solving Quadratic Equations by Factoring
In this section we will learn how to:
Write quadratic equations in intercept form
Solve quadratic equations by factoring

3. 5.3 – Solving Quadratic Equations by Factoring
Intercept form – of a quadratic equation is
y = a(x – p)(x – q)
p and q represent the x-intercepts of the graph corresponding to the equation

4. 5.3 – Solving Quadratic Equations by Factoring
Changing a quadratic in intercept form to standard forms requires using the FOIL method
First
Outer
Inner
Last
Multiply the terms: first, outer, inner, last
Combine any like terms

5. 5.3 – Solving Quadratic Equations by Factoring
Example 1
(6x + 1)(2x – 4)

6. 5.3 – Solving Quadratic Equations by Factoring
Example 2
(-3x + 5)(3x + 2)

7. 5.3 – Solving Quadratic Equations by Factoring
Example 3
(9x – 2)2

8. 5.3 – Solving Quadratic Equations by Factoring
Example 4
(6x + 3)2

9. 5.3 – Solving Quadratic Equations by Factoring
Example 5
(x + 7)3

10. 5.3 – Solving Quadratic Equations by Factoring
Example 6
(2x + 4)3

11. 5.3 – Solving Quadratic Equations by Factoring
Example 7
(3x – 1)3

12. 5.3 – Solving Quadratic Equations by Factoring
HOMEWORK
5.3 Part 1 Worksheet

13. 5.3 – Solving Quadratic Equations by Factoring
Find the Greatest Common Factor (GCF)
If all the terms of a polynomial have a factor(s) in common, you can factor out that greatest common factor

14. 5.3 – Solving Quadratic Equations by Factoring
Example 1
Factor out the GCF
8y2 + 16y5 =
6a4 – 8a2 + 2a =
-15x3y + 9x2y7 =
-5x2y – x2 + 3x3y5 + 11x7 =

15. 5.3 – Solving Quadratic Equations by Factoring
CLASSWORK
5.3 Part 2 Practice

16. 5.3 – Solving Quadratic Equations by Factoring
Factoring a Difference of Perfect Squares
If you have a quadratic equation that has the difference of two terms that are both perfect squares, it factors as:
A2 – B2 = (A + B)(A – B)

17. 5.3 – Solving Quadratic Equations by Factoring
Example 1
Factor:
x2 – 9 =
4x2 – 25 =
9x2 – 16y2 =

18. 5.3 – Solving Quadratic Equations by Factoring
Example 2
Factor:
100x2 – 81y2 =
3x2 – 75 =
20x2 – 5y2 =

19. 5.3 – Solving Quadratic Equations by Factoring
Factoring a Trinomial
Ax2 ± Bx + C =
ADD inner and outer to get B
( ) ( + )
( ) ( )

20. 5.3 – Solving Quadratic Equations by Factoring
Example 1
Factor:
x2 + 10x + 9
x2 + 8x + 15
x2 – 10x + 25

21. 5.3 – Solving Quadratic Equations by Factoring
Example 2
Factor:
x2 – 2x + 1
x2 – 14x + 24
x2 + 6x + 9

22. 5.3 – Solving Quadratic Equations by Factoring
HOMEWORK 5.3 Part 3 Practice

23. 5.3 – Solving Quadratic Equations by Factoring
Factoring a Trinomial
Ax2 ± Bx - C =
SUBTRACT inner and outer to get B
( ) ( - )
( ) ( )

24. 5.3 – Solving Quadratic Equations by Factoring
Example 1
Factor:
x2 – 3x – 18
x2 + 5x – 6
x2 – 2x – 35

25. 5.3 – Solving Quadratic Equations by Factoring
Example 2
Factor:
x2 + 4x – 21
x2 + x – 20
x2 – 4x – 5

26. 5.3 – Solving Quadratic Equations by Factoring
HOMEWORK 5.3 Part 4 Worksheet

27. 5.3 – Solving Quadratic Equations by Factoring
Factoring a Trinomial
Ax2 ± Bx + C
( ) ( )
( ) ( )
Ax2 ± Bx – C
( ) ( )
( ) ( )

28. 5.3 – Solving Quadratic Equations by Factoring
Example 1
Factor:
2x2 + 3x + 1
5x2 – 28x – 12

29. 5.3 – Solving Quadratic Equations by Factoring
Example 2
Factor:
4x2 – 12x + 5
3x2 + 2x – 16

30. 5.3 – Solving Quadratic Equations by Factoring
Example 3
Factor:
4x2 – 14x + 10
15x2 + 18x – 24

31. 5.3 – Solving Quadratic Equations by Factoring
Example 4
Factor:
25x2 – 10x – 3
3x2 + 11x + 6

32. 5.3 – Solving Quadratic Equations by Factoring
HOMEWORK 5.3 Part 5 Worksheet

33. 5.3 – Solving Quadratic Equations by Factoring
CLASSWORK 5.3 Graded Worksheet

34. 5.3 – Solving Quadratic Equations by Factoring
Solving by Factoring
If the equation is not equal to zero, rewrite so that it is
Factor out a GCF if possible
You now have one of the following:
A trinomial that must be factored (x2 + Bx + C)
A difference of two squares that must be factored (x2 – C)
Two expressions
Set each of the remaining expressions equal to zero and solve

35. 5.3 – Solving Quadratic Equations by Factoring
Example 1
Factor and solve:
x2 + 13x + 30 = 0
x2 + 5x – 24 = 0

36. 5.3 – Solving Quadratic Equations by Factoring
Example 2
Factor and solve:
x2 – 13x = -22
x2 – 2x = 48

37. 5.3 – Solving Quadratic Equations by Factoring
Example 3
Factor and solve:
x2 – 100 = 0
2x2 – 72 = 0

38. 5.3 – Solving Quadratic Equations by Factoring
Example 4
Factor and solve:
x2 + 15x = 0
2x2 – 6x = 0

39. 5.3 – Solving Quadratic Equations by Factoring
HOMEWORK 5.3 Worksheet

40. 5.3 – Solving Quadratic Equations by Factoring
CLASSWORK 5.3 Graded Worksheet