Rewrite Rational Expressions (Long Division)
These lessons, with videos, examples and step-by-step solutions, help High School students learn how to rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
Related Pages
Synthetic Division
Common Core Algebra
Common Core Mathematics
Suggested Learning Targets
-
Rewrite rational expressions,
a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) by using factoring, long division, or synthetic division. -
Use a computer algebra system for complicated examples to assist with building a broader conceptual understanding.
Common Core: HSA-APR.D.6
Rewriting simple rational expressions in different forms (Common Core A-APR.6)
Polynomial Division: Long Division.
Ex 1: Divide a Trinomial by a Binomial Using Long Division
This video provides two basic examples of how to divide a degree two trinomial by a degree one binomial.
Ex 2: Divide a Polynomial by a Binomial Using Long Division
This video provides an example of how to perform long division by dividing a degree three polynomial by a degree one binomial. There are no missing terms in the dividend. The quotient has a remainder.
Ex 3: Divide a Polynomial by a Binomial Using Long Division
This video provides an example of how to perform long division by dividing a degree three polynomial by a degree one binomial. There are missing terms in the dividend. The quotient has a remainder.
Ex 4: Divide a Polynomial by a Binomial Using Long Division
This video provides an example of how to perform long division by dividing a degree three polynomial by a degree one binomial. There are missing terms in the dividend. The quotient has no remainder.
Ex 5: Divide a Polynomial by a Binomial Using Long Division
This video provides an example of how to perform long division by dividing a degree three polynomial by a degree one binomial. There are missing terms in the dividend. The quotient has fractional coefficients and there is a remainder.
Ex 6: Divide a Polynomial by a Degree Two Binomial Using Long Division
This video provides an example of how to perform long division by dividing a degree three polynomial by a degree two binomial. The quotient has a remainder.
Check out our most popular games!
Fraction Concoction Game:
Master fractions in the lab: mix, add, and subtract beakers to create the perfect concoction!
Fact Family Game:
Complete fact families and master the link between addition & subtraction and multiplication & division.
Number Bond Garden:
Clear the board by matching number pairs that sum to ten in this garden-themed mental math puzzle.
Online Addition Subtraction Game:
Practice your addition and subtraction skills to help the penguin find its mummy.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.