1. 6.2 Polynomials and Linear Factors
At the end of this lesson, you should be able to:
Factor sums and differences of cubes
Solve a polynomial equation by factoring
Write a polynomial function from its zeros

2. Factoring the Sums and Differences of Cubes
13 = _
23 = _
33 = _
43 = _
53 = _
63 = _
73 = _
83 = _
93 = _
103 = _ 1 8 27 64
125
216
343
512
729
1000
Being familiar with perfect cubes will make cubing binomials and factoring sums and differences of cubes easier.

3. Special Factoring Patterns
…more know-by-♥ stuff!
Special Factoring Patterns
Sum of Two Cubes
u3 + v3 =
Example:
u =
Difference of Two Cubes
u3 - v3 =
u =
(u + v) (u2 - uv + v2)
(u - v) (u2 + uv + v2)

4. Factor the polynomials:
a. x3 - 27
b. x3 - 64
c. x
d. x
e. 4x
f. 3x

5. REVIEW: FACTORING BY GROUPING
Factor the polynomials:
a. 4x3 - 6x2 + 10x – 15
b. x3 - 2x2 - 4x + 8

6. REVIEW: Factoring By Using Combined Methods
Factor the polynomial COMPLETELY:
2x x2 + 12X

7. ZERO PRODUCT PROPERTY Recall: Let a and b be real numbers.
If ab = 0, then a = 0 or b = 0.
Alert!
This property connects factoring to solving equations!

8. SOLVING POLYNOMIAL EQUATIONS BY FACTORING
Solve the following equations by factoring:
a. 3x4 = 48x2
b. x
c. 5x

9. FACTOR THEOREM
You can reverse the process and write the linear factors when you know the zeros (solutions). The relationship between the linear factors of a polynomial and the zeros of a polynomial is given by the Factor Theorem.
The expression x – a is a linear factor of a polynomial if and only if the value a is a zero of the polynomial function.
Write the factors of a polynomial whose zeros are 2, 2, & -3.

10. WRITING A POLYNOMIAL FUNCTION FROM ITS ZEROS
Alert!
A repeated zero is called a multiple zero. A multiple zero has a multiplicity equal to the number of times the zero occurs.
What is the multiplicity of the polynomial
function? Explain.

11. Final Checks for Understanding
Given x3 - 4x2 = - 4x, determine the following:
Factors:
__________________
Solutions:
X-intercepts:
Zeros:

12. Homework
Connections: Zeros, Factors, and Solutions WS, plus text_______________