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Polynomial Division and Rational Expressions
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Algebra
Polynomial Division and Rational Expressions
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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 singleterm factors and finishing all our factoring, the next thing we do to divide polynomials is use good oldfashioned long division. You know, oldfashioned like the donut: de...
Common Factors
The first thing to do when dividing polynomials is to look for and remove common factors. In terms of rational expressions, "looking for common factors" means that we're looking for those that go i...
Factoring
After looking for singleterm 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.W...
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...
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 nastylooking ratio...
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 are actually solving a...
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