1. Factoring Quadratic Expressions
Section 5.4
Factoring Quadratic Expressions

2. Finding Common and Binomial Factors
Definition 1: Factoring is rewriting an expression as the product of its factors.
Definition 2: The greatest common factor (GCF) is a common factor of the terms of the expression.

3. Examples 1 – 3 Factor each expression. 4 𝑥 2 +20𝑥−12 9 𝑛 2 −24𝑛
9 𝑥 2 +3𝑥−18

4. Examples 4 & 5
Factor each expression.
7 𝑝 2 +21
4 𝑤 2 +2𝑤

5. Examples 6 & 7
Factor each expression.
𝑥 2 +8𝑥+7
𝑥 2 +6𝑥+8

6. Examples 8 & 9
Factor each expression.
𝑥 2 +12𝑥+32
𝑥 2 +14𝑥+40

7. TOTD
Factor each expression.
15x² + 25x + 100
8m² + 4m

8. Examples 10 – 11
Factor each expression.
𝑥 2 −17𝑥+72
𝑥 2 −6𝑥+8

9. Examples 12 – 13
Factor each expression.
𝑥 2 −7𝑥+12
𝑥 2 −11𝑥+24

10. Examples 14 – 15
Factor each expression.
𝑥 2 −𝑥−12
𝑥 2 −14𝑥−32

11. Examples 16 – 17
Factor each expression.
𝑥 2 +3𝑥−10
𝑥 2 +4𝑥−5

12. Examples 18 – 19
Factor each expression.
3 𝑥 2 −16𝑥+5
2 𝑥 2 +11𝑥+12

13. Examples 20 – 21
Factor each expression.
4 𝑥 2 +7𝑥+3
2 𝑥 2 −7𝑥+6

14. TOTD
Factor.
x² + 10x + 24
x² - 14x + 33

15. Examples 22 – 23
Factor each expression.
4 𝑥 2 −4𝑥−15
2 𝑥 2 +7𝑥−9

16. Examples 24 – 25
Factor each expression.
3 𝑥 2 −16𝑥−12
4 𝑥 2 +5𝑥−6

17. Factoring Special Expressions
Definition 3: A perfect square trinomial is the product you obtain when you square a binomial.

18. Examples 26 – 27
Factor each expression.
9 𝑥 2 −42𝑥+49
64 𝑥 2 −16𝑥+1

19. Examples 28 – 29
Factor each expression.
4 𝑥 2 +12𝑥+9
25 𝑥 2 +90𝑥+81

20. Difference of Squares
An expression of the form a2 – b2 is defined as the difference of two squares.

21. Examples 30 & 31
Factor each expression.
𝑥 2 −64
4 𝑎 2 −49

22. TOTD
Factor each expression completely.
m² + 11m + 18
3x² + 5x - 50