# Polynomial Division and Rational Expressions Exercises

#### Common Factors

The easiest case of polynomial division is when the divisor is a single term that happens to be a common factor of the dividend. You'll love when this happens. For the sake of the integer analogy,...

#### Factoring

Factoring isn't only for when the divisor is a single term. We can use factoring to divide one polynomial by another polynomial, as long as the polynomial in the denominator is a factor of the poly...

#### Long Division

After looking for single-term factors and finishing all our factoring, the next thing we do to divide polynomials is use good old-fashioned long division. You know, old-fashioned like the donut: de...

#### Rational Expressions

Rational expressions are nothing to be afraid of. Don't let the bared fangs and red, glowing eyes fool you. Despite the scary drooling, they're only a particular type of expression. The eyes are...

#### Common Factors

The first thing to do when dividing polynomials is to look for and remove any common monomial factors. In terms of rational expressions, "looking for common factors" means that we're looking for...

#### Factoring

After looking for single-term common factors, the next thing to do is to factor the numerator and denominator to see if there are any other factors we can cancel. We're on an absolute canceling tea...

#### Long Division

Once we've canceled all the factors we can, we write out the new numerator and denominator (the unfactored versions) and look at their degrees. If it's too many degrees, we'll stay inside and eat c...

#### A Clever Trick

First, you take the rubber ball in your left hand, then tap the back of that hand with the wand held in your right. Say a few magic words, and then...oh. This isn't amateur magician hour? Our bad...

#### Simplifying Complex Rational Expressions

A complex rational expression is a rational expression in which the numerator and/or the denominator are rational expressions. In other words, a complex rational expression is a nasty-looking rat...

#### Equations Involving Rational Expressions

Solving an equation that contains rational expressions is similar to solving any old equation that has fractions in it. In fact, if the variable only occurs in numerators, we actually are solving...