1. 7.3 Products and Factors of Polynomials
Objectives
Multiply polynomials, and divide one polynomial by another by using long division and synthetic division.
Use the Remainder and Factor Theorems to solve problems.

2. Glossary Terms Factor Theorem long division Remainder Theorem
7.3 Products and Factors of Polynomials
Glossary Terms
Factor Theorem
long division
Remainder Theorem
synthetic division

3. Rules and Properties a3 + b3 = (a + b)(a2 – ab + b2)
7.3 Products and Factors of Polynomials
Rules and Properties
Factoring the Sum and Difference of Two Cubes
a3 + b3 = (a + b)(a2 – ab + b2)
a3 – b3 = (a – b)(a2 + ab + b2)

4. x + 3 is a factor because the remainder is 0.
7.3 Products and Factors of Polynomials
Key Skills
Use long division to find factors and remainders of polynomials. x2
+ 3x
+ 2
Is x + 3 a factor of x3 + 6x2 + 11x + 6?
x + 3
x3 + 6x2 + 11x + 6
x3 + 3x2
3x2 + 11x
3x x
x + 3 is a factor because the remainder is 0.
2x + 6
2x + 6

5. 7.3 Products and Factors of Polynomials
Key Skills
Use synthetic division to find factors and remainders of polynomials.
Is x – 3 a factor of x3 – 3x2 + x + 6? 3
1 –3 1 6 3 3
x – 3 is not a factor by the Remainder Theorem (because the remainder is 9). 1 1 9
TOC