Topic: Exponents and Polynomials
Subtopic: Polynomial Operations III - Divide & Long Divide
Overview
Concluding our work with polynomials, in this lesson we focus on division of polynomials including the long division. This will lead nicely into a topic in Intermediate Algebra involving rational (fractional) expressions.
Objectives
By the end of this topic you should know and be prepared to be tested on:
- 6.4.1 Divide a monomial by a monomial carefully cancelling like factors
- 6.4.2 Divide a polynomial by a monomial via two methods: (1) factoring common factors from the numerator and reducing the fractional expression, or (2) splitting the fractional expression into a sum of smaller fractions and reducing each one separately
- 6.4.3 Long divide a binomial (or larger polynomial) into a trinomial (or larger polynomial)
Terminology
Define: reducing a fractional expression, long division of polynomials
Text Notes
Text:
Intro & Inter Algebra for CS 3ed by Blitzer, sect. 5.5-5.6
- ch 5.5 covers dividing polynomials by monomials and also discusses a "zero exponent".
- ch 5.5 pg 361-262 Pay attention to the two cautions in the yellow boxes. They describe very common errors!
- ch 5.6 covers simplifying rational expressions (fractions with a polynomial in the numerator and a polynomial in the denominator) via long division.
- ch 5.6 SKIP "synthetic division" as shown on pg 373-375 and example 5.