1. Section 6.4: Factoring Polynomials
Chapter 6: Polynomials
Section 6.4: Factoring Polynomials

2. Section 6.4: Factoring Polynomials
Goals: To factor a polynomial with terms containing common factors; to factor a perfect square trinomial, a difference of squares, and a sum or difference of cubes

3. Section 6.4: Factoring Polynomials
Find the Greatest Common Factor (GCF)
If all the terms of a polynomial have a factor(s) in common, you can factor out that greatest common factor

4. Section 6.4: Factoring Polynomials
Example
Factor out the GCF
8y2 + 16y5 =
6a4 – 8a2 + 2a =
-15x3y + 9x2y7 =
-5x2y – x2 + 3x3y5 + 11x7 =

5. Section 6.4: Factoring Polynomials
Factoring a Difference of Perfect Squares
If you have a quadratic equation that has the difference of two terms that are both perfect squares, it factors as:
A2 – B2 = (A + B)(A – B)

6. Section 6.4: Factoring Polynomials
Example
Factor:
x2 – 9 =
4x2 – 25 =
9x2 – 16y2 =

7. Section 6.4: Factoring Polynomials
Example
Factor:
100x2 – 81y2 =
3x2 – 75 =
20x2 – 5y2 =

8. Section 6.4: Factoring Polynomials
Factoring a Perfect Square Trinomial
A perfect square trinomial has two identical binomial factors
a2 + 2ab + b2 = (a + b)2
a2 – 2ab + b2 = (a – b)2

9. Section 6.4: Factoring Polynomials
Example
Factor
y2 + 4y + 4 =
x2 – 14x + 49 =
a2 + 22ab + 121b2 =
2x2 – 20x + 50 =

10. Section 6.4: Factoring Polynomials
Factoring a Sum or Difference of Two Cubes
The sum or difference of two cubes can be factored as the product of a binomial and a trinomial
a3 + b3 = (a + b)(a2 – ab + b2)
a3 – b3 = (a – b)(a2 + ab + b2)

11. Section 6.4: Factoring Polynomials
Example
Factor
x3 + 8
27y3 – 125
a3b3 – c3

12. Section 6.4: Factoring Polynomials
Example
Factor
64x3 + y3
2w3 – 432

13. Section 6.4: Factoring Polynomials
Homework:
Practice Exercises: Pg. 273 #2-42 (even)