- Topics At a Glance
- Exponents
- Negative Exponents
- Fractional Exponents
- Irrational Exponents
- Variables as Exponents
- Defining Polynomials
- Degrees of a Polynomial
- Multivariable Polynomials
- Degrees of Multivariable Polynomials
- Special Kinds of Polynomials
- Evaluating Polynomials
- Roots of a Polynomial
- Combining Polynomials
**Multiplying Polynomials**- Multiplication of a Monomial and a Polynomial
- Multiplication of Two Binomials
- Special Cases of Binomial Multiplication
- General Multiplication of Polynomials
**We'll Divide Polynomials Later!**- Factoring Polynomials
- The Greatest Common Factor
- Recognizing Products
- Trial and Error
- Factoring by Grouping
- Summary
- Introduction to Polynomial Equations
- Solving Polynomial Equations
- In the Real World
- I Like Abstract Stuff; Why Should I Care?
- How to Solve a Math Problem

Polynomials and integers have many similarities, but when it comes to dividing, they each go their own way. You might even say they "divide." Ooh, see what we did there?

If we add any two integers, subtract one integer from another, or multiply two integers, we always find an answer that's also an integer. When we divide one integer by another, however, we don't necessarily have an integer. We might find a rational number. It would be nice if division followed the example set by addition, subtraction, and multiplication instead of being a pain in the hiney, but there's always one...

It's the same deal with polynomials. If we take the difference of any two polynomials or multiply two polynomials, we get an answer that's *also* a polynomial. When we try to divide one polynomial by another, however, the answer won't necessarily be a polynomial. "1" is a polynomial, and "*x*" is a polynomial, but is not a polynomial. This is an example of a **rational function**, which we'll talk more about in the next unit. Sorry, we don't mean to be such a tease.