1. Keeper 1 Honors Calculus
Factoring
Keeper 1
Honors Calculus

2. What does it mean to "factor?"
Take an addition or subtraction problem and write it as an EQUIVALENT multiplication problem.

3. To factoring using GCF:
Step 1: Determine the greatest common factor of the given terms. The greatest common factor or GCF is the largest factor that all terms have in common. Step 2: Factor out (or divide out) the greatest common factor from each term. ***You could check your answer at the point by distributing the GCF to see if you get the original question. ***Factoring out the GCF is the first step in many factoring problems.

4. Example: Factor using GCF.
12 𝑥 3 +16

5. Example: Factor using GCF.
9 𝑥 3 −27𝑥+36

6. Example: Factor using GCF.
2𝑥+5

7. Factoring Quadratic Trinomials where 𝑎=1
Identify the a, b, and c in the trinomial 𝑎 𝑥 2 +𝑏𝑥+𝑐.
Identify two numbers that multiply to 𝑐 and add to 𝑏
Substitute the two numbers into two binomials.
Write your answer as:
(x ___)(x ___)
There are only 4 possible sign combinations for these trinomials.
Don't forget to ALWAYS start by looking for a GCF!

8. Example: Factor
𝑥 2 +10𝑥+24

9. Example: Factor
𝑥 2 −5𝑥−14

10. Example: Factor
𝑥 2 −7𝑥+10

11. Example: Factor
𝑥 2 +𝑥−20

12. Putting it all together!
Example: Factor
5 𝑥 2 +35𝑥+60

13. How to Factor when 𝑎≠1 1.) Multiply "𝑎" and "𝑐"
2.) Determine what 2 numbers multiply to "𝑎𝑐" that sum to "𝑏"
3.) Rewrite "𝑏" as those 2 numbers (include the variable)
You should now have 4 terms!
4.) Factor by grouping.
*Put (first 2 terms)(last 2 terms)
*Factor out a GCF from each parenthesis.
GCF(leftovers) +/- GCF(leftovers)
*Your leftovers should be identical!
*Write your factors as (GCF's)(leftover)
Remember to always start by checking for a GCF of the ENTIRE problem first!

14. Example: Factor
2 𝑥 2 +11𝑥+12

15. Example: Factor
8 𝑥 2 +2𝑥−3

16. Example: Factor
−5 𝑥 2 −7𝑥+6

17. Difference of Squares
We use DOS when you have… 𝑎 2 − 𝑏 2 *2 Terms *1 Minus Sign *Coefficients and Constants are Perfect Squares *Variables have even exponents

18. Difference of Squares
Take the square root of each term. Write your answer as: (𝑎+𝑏)(𝑎−𝑏)

19. Example: Factor
𝑥 2 −25

20. Example: Factor
4 𝑥 2 −49

21. You Try!!!
30 𝑎 2 −111𝑎+90

22. You Try!!!
10 𝑝 2 +57𝑝+54

23. You Try!!!
18 𝑚 2 −50𝑚𝑛−12 𝑛 2

24. You Try!!!
9 𝑥 2 +4

25. You Try!!!
169 𝑣 4 −1

26. You Try!!!
1452 𝑛 8 −1728 𝑛 2

27. You Try!!!
−8 𝑥 3 +64

28. Sums and Difference of Cubes

29. Example: Factor 𝑥

30. Example: Factor
8 𝑥 3 −27

31. Example: Factor
2𝑥 𝑦 3