Monomial Factors of Polynomials Chapter 5 Section 5.3

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

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

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

Example 5m + 35 5

Example 26uv – 39v 13v

Example 3x4 – 9x3y + 6x2y2 -3x2

Example x3y – 4x + 6y xy

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.

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

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)

Example Factor 5x2 + 10x

Example Factor 4x5 – 6x3 + 14x

Example Factor 8a2bc2 – 12ab2c2

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.

Questions

Assignment Worksheet