1. 5.4 Factoring Polynomials1
Methods 2
Examples 3
Practice Problems

2. Definition
If a polynomial is a product of other polynomials, then each polynomial in the product is a factor
Factors that contain polynomials of a positive degree are called nontrivial factors
Polynomials than cannot be factored are referred to as prime or irreducible

3. Greatest Common Factor (GCF)
Look for the largest common number and/or variables in each term
Divide each term by the common terms

4. Grouping

5. Rainbow Method (2nd degree Polynomial)

6. Simplifying Quotients
Factor the numerator
Factor the denominator
Cancel any like polynomials

7. Special Cases Difference of two Squares: x2 – y2 = (x + y)(x - y)
Factoring Formulas
Example
Difference of two Squares:
x2 – y2 = (x + y)(x - y)
9a2 – 16
=(3a)2 – (4)2
= (3a + 4)(3a – 4)
Difference of two Cubes:
x3 – y3 = (x - y)(x2 + xy + y2)
8a3 – 27
= (2a)3 – (3)3
= (2a – 3)[(2a)2 + (2a)(3) + (3)2]
=(2a – 3)(4a2 + 6a + 9)
Sum of two Cubes:
x3 + y3 = (x + y)(x2 – xy + y2)
125a3 + 1
= (5a)3 + (1)3
= (5a + 1)[(5a)2 – (5a)(1) + (1)2]

8. Practice Problems
Page 242
Problems 5-11, odd
15-37, odd
46-51