1. Chapter 6 – Polynomials and Polynomial Functions
6.5 – Factoring Cubic Polynomials

2. 6.5 – Factoring Cubic Polynomials
Today we will be learning how to:
Factor cubic polynomials and solve cubic equations

3. 6.5 – Factoring Cubic Polynomials
Special Product Patterns
Sum of Two Cubes
a3 + b3 + (a + b)(a2 – ab + b2)
x3 + 8 =
Difference of Two Cubes
a3 – b3 = (a – b)(a2 + ab + b2)
27x3 – 1 =

4. 6.5 – Factoring Cubic Polynomials
Example 1
27x
Factor d3 – 125

5. 6.5 – Factoring Cubic Polynomials
Example 2
Factor 10x4 – 10
3m m7 – 51m2

6. 6.5 – Factoring Cubic Polynomials
Example 3
An open concrete block has four sides and a bottom, but no top. The volume of concrete in the block can be modeled by the expression 2x3 – 8x2 + 10x – 4, where x is the thickness of the concrete. Factor the expression.

7. 6.5 – Factoring Cubic Polynomials
HOMEWORK 6.5 Worksheet #1 – 18

8. 6.5 – Factoring Cubic Polynomials
Factor by Grouping
Some polynomials you can factor by grouping
Pairs of terms that have common monomial factors
ra + rb + sa + sb = r(a + b) + s(a + b)
= (r + s)(a + b)

9. 6.5 – Factoring Cubic Polynomials
Example 4
Factor
x3 + 4x2 – 36x – 144
4x2(x – 3) – 25(x – 3)

10. 6.5 – Factoring Cubic Polynomials
Homework
6.5 Worksheet #

11. 6.5 – Factoring Cubic Polynomials
Solving Cubic Equations
In section 5.3 we found the zeros(roots) of some quadratics by setting them equal to zero, factoring, then solving each for x.
We can do the same for some cubic equations

12. 6.5 – Factoring Cubic Polynomials
Example 5
Solve 3x3 – 6x = -3x2

13. 6.5 – Factoring Cubic Polynomials
Example 6
x3 + 5x2 – 3x = 15

14. 6.5 – Factoring Cubic Polynomials
HOMEWORK 6.5 Worksheet #25 – 39 EXTRA CREDIT #