Chapter 6 – Polynomials and
Polynomial Functions
6.5 – Factoring Cubic Polynomials
6.5 – Factoring Cubic
Polynomials

Today we will be learning how to:

Factor cubic polynomials and solve cubic
equations
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 =
6.5 – Factoring Cubic Polynomials

Example 1

Factor d3 – 125

27x3 + 216
6.5 – Factoring Cubic Polynomials

Example 2

Factor
10x4
– 10

3m12 + 48m7 – 51m2
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.
6.5 – Factoring Cubic Polynomials
HOMEWORK
6.5 Worksheet
#1 – 18
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)
6.5 – Factoring Cubic Polynomials

Example 4

Factor
 4x2(x
– 3) – 25(x – 3)

x3 + 4x2 – 36x – 144
6.5 – Factoring Cubic
Polynomials
Homework
6.5 Worksheet
#19 - 24
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
6.5 – Factoring Cubic
Polynomials

Example 5

Solve 3x3 – 6x = -3x2
6.5 – Factoring Cubic Polynomials

Example 6

x3 + 5x2 – 3x = 15
6.5 – Factoring Cubic Polynomials
HOMEWORK
6.5 Worksheet
#25 – 39
EXTRA CREDIT
#31 - 33