1. Unit 2: Expressions and Polynomials
GCF and Factoring

2. GCF Greatest Common Factor
The largest factor in common between two numbers
Ex: The GCF between 25 and 30 is 5
Ex: The GCF between 4x and 10 is 2
Ex: The GCF between 5mnp and 15mp is 5mp

3. GCF and Factoring
Factor the GCF out of the following polynomial

4. Factoring Polynomials
Review:

5. Factoring Polynomials Bottoms Up!
To factor polynomials in the form
Use the Bottoms Up Method
This method works for factoring any type of polynomial!

6. Bottoms Up! Steps Step 1: Multiply a and c together
Step 2: Find 2 number that multiply to give (ac) and add to give b
Step 3: Place each of those numbers inside of separate binomials with x at the beginning
Step 4: Divide each of the constants by a
Step 5: If any constant is in fraction form, multiply each term in that binomial by the denominator

7. Factoring Polynomials: Bottoms Up!
Example:
Factor
Step 1: Multiply a and c together
1 x 45 = 45
Step 2: Two numbers that multiply to give 45 and add to give 14
9 and 5
Step 3: Place each number inside of binomials
(x + 9) (x + 5)
Step 4: Divide each of the constants by a
a equals 1, so there is no need to divide further.
Your answer is (x + 9)(x + 5)

8. Factoring Polynomials: Bottoms Up!
Factor the following polynomial:
Step 1: Multiply a and c together
2 x 18 = 36
Step 2: Two numbers that multiply to give 36 and add to give 15
12 and 3
Step 3: Place each number inside of binomials
(x + 12) (x + 3)

9. Factoring Polynomials: Bottoms Up!
Step 4: Divide each of the constants by
Step 5: Since is not an integer, multiply the 2nd binomial by 2 to get rid of the fraction.
Your final answer is

10. Try!
Factor the following: 1) 2)