1. Factoring Simple Polynomials

2. Definitions
Factors of a number are the numbers that divide the original number evenly.
Writing a number as a product of factors is called a factorization of the number.
The prime factorization of a number is the factorization of that number written as a product of prime numbers.
Common factors are factors that two or more numbers have in common.
The Greatest Common Factor (GCF) is the largest common factor.

3. Ex: Find the GCF(24, 40). Prime factor each number: 24 2 12 2 6 2 3
 24 = 2*2*2*3 = 23*3
 GCF(24,40)
= 23 = 8 40 2 20 2 10 2 5
 40 = 2*2*2*5 = 23*5

4. The Greatest Common Factor of terms of a polynomial is the largest factor that the original terms share
Ex: What is the GCF(7x2, 3x)
7x2 = 7 * x * x
3x = 3 * x
The terms share a factor of x
 GCF(7x2, 3x) = x

5. Greatest Common Factors aka GCF’s
Find the GCF for each set of following numbers.
Find means tell what the terms have in common.
Hint: list the factors and find the greatest match.
2, 6
-25, -40
6, 18
16, 32
3, 8 2 -5 6 16 1
No common factors? GCF =1

6. Greatest Common Factors aka GCF’s
Find the GCF for each set of following numbers.
Hint: list the factors and find the greatest match.
x, x2
x2, x3
xy, x2y
2x3, 8x2
3x3, 6x2
4x2, 5y3 x x2 xy
2x2
3x2 1
No common factors? GCF =1

7. Greatest Common Factors aka GCF’s
Factor out the GCF for each polynomial: Factor out means you need the GCF times the remaining parts.
How can you check?
a) 2x + 4y
5a – 5b
18x – 6y
2m + 6mn
5x2y – 10xy
2(x + 2y)
5(a – b)
6(3x – y)
2m(1 + 3n)
5xy(x - 2)

8. FACTORING by GCF Take out the GCF EX: 15xy2 – 10x3y + 25xy3 How:
Find what is in common in each term and put in front. See what is left over.
Check answer by distributing out.
Solution:
5xy( )
3y – 2x2 + 5y2

9. FACTORING Take out the GCF EX: 2x4 – 8x3 + 4x2 – 6x How:
Find what is in common in each term and put in front. See what is left over.
Check answer by distributing out.
Solution: 2x
(x3 – 4x2 + 2x – 3)

10. Ex: Factor 6a5 – 3a3 – 2a2 Recall: GCF(6a5,3a3,2a2)= a21
6a5 – 3a3 – 2a2 = a2( )
6a3 3a 2 a2 a2 a2
 6a5 – 3a3 – 2a2 = a2(6a3 – 3a – 2)