1. Algebra 1
Section 10.1

2. Factoring
Factoring is the process of determining individual factors of a product.
We will start by finding greatest common factors.

3. Example 1
108 = 2 • 2 • 3 • 3 • 3
72 = 2 • 2 • 2 • 3 • 3
GCF = 2 • 2 • 3 • 3 = 36
15x = 3 • 5 • x
42x2y = 2 • 3 • 7 • x • x • y
GCF = 3 • x = 3x

4. Definitions
The greatest common factor of a polynomial is the product of all factors shared by every term of the polynomial.
Two numbers or terms are considered relatively prime if their GCF is 1.

5. Example 2 Factor 8x2 – 16. 8x2 = 2 • 2 • 2 • x • x 16 = 2 • 2 • 2 • 2
GCF = 2 • 2 • 2 = 8

6. Example 2 Factor 8x2 – 16. GCF = 2 • 2 • 2 = 8
Factor 8 from each term.
8(x2) – 8(2)
8(x2 – 2)

7. Factoring Common Monomials from a Polynomial
Find the GCF of all terms in the polynomial.
Divide the GCF out of each term (applying the Distributive Property in reverse).

8. Factoring Common Monomials from a Polynomial
Write the factorization as the GCF times the sum of the quotients.
Check your solution by multiplying the two factors.

9. Example 3 Factor 42a3 + 14a. 42a3 = 2 • 3 • 7 • a • a • a
GCF = 2 • 7 • a = 14a

10. Example 3 Factor 42a3 + 14a. GCF = 2 • 7 • a = 14a
Factor 14a from each term.
14a(3a2) + 14a(1)
14a(3a2 + 1)

11. Example 4 Factor 36x2y + 9xy3 – 27xy. GCF = 9xy
9xy(4x) + 9xy(y2) – 9xy(3)
9xy(4x + y2 – 3)

12. Example 5 Factor 51x3 + 26y. GCF = 1
Since the two terms are relatively prime, the polynomial is prime and will not factor.

13. Factoring A polynomial can contain a common binomial factor.
3(x + y) – y(x + y)
(x + y)(3 – y)

14. Example 6 Factor x(x + 1) + 2(x + 1).
(x + 1) is a factor of each term.
(x + 1)(x + 2)

15. Homework: pp