**Lawrence Neff Stout
Professor of Mathematics
Illinois Wesleyan University
Bloomington, IL**

Basic algebra is a native language of most mathematicians; many students don't speak it fluently. Fluency comes with many years of practice. This guide is intended to provide a refresher on some algebraic manipulations which arise often in calculus. It doesn't cover everything and it doesn't provide the practice you may need. I've included a subsection on common errors in each of the sections here- try to avoid the pitfalls I've identified.

- Manipulation of fractions
- Addition, subtraction, multiplication, and division
- Finding simpler forms by cancellation of common factors
- Common errors

- Factoring and division of polynomials
- Long division of polynomials
- The remainder, factor, and rational roots theorems
- Common factorization situations
- Using factorization backwards

- Solving equations and inequalities
- Linear equations
- Quadratic formula
- Higher degree equations
- Finding when a rational function is positive

- Handling exponents
- Knowing when to combine terms
- Properties of absolute values
- About this document ...

Larry Stout 2003-01-09