1. Monomial Factors of Polynomials
Chapter 5
Section 5.3

2. Objective
Students will divide polynomials by monomials and find monomial factors of polynomials

3. Concept
In a previous lesson we proved that if a, b, and c are real numbers and c ≠ 0, then a + b = a + b c c c This result if also true when a, b, and c are monomials and c ≠ 0

4. Concept
To divide a polynomial by a monomial, divide each term of the polynomial by the monomial and add the results

5. Example 5m

6. Example
26uv – 39v 13v

7. Example
3x4 – 9x3y + 6x2y2 -3x2

8. Example
x3y – 4x + 6y xy

9. Concept
We say that one polynomial is evenly divisible, or just divisible, by another polynomial if the quotient is also a polynomial. The last example shows that x3y – 4x + 6y is not divisible by xy because the quotient is not a polynomial.

10. Concept
You factor a polynomial by expressing it as a product of other polynomials. The factor set for a polynomial having integral coefficients is the set of all polynomials having integral coefficients. This means that you use the GCF between all terms

11. Concept
The following steps will help you factor using the greatest monomial factor of the polynomial: 1. Find the GCF of all terms 2. Divide the polynomial by the GCF 3. Answer GCF(quotient)

12. Example
Factor 5x2 + 10x

13. Example
Factor 4x5 – 6x3 + 14x

14. Example
Factor 8a2bc2 – 12ab2c2

15. Concept
Hopefully with a little practice you will be able to do the division steps mentally. Also you should always check your factorization by multiplying the resulting factors. After multiplying you should always end with the polynomial you started with.

16. Questions

17. Assignment
Worksheet