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
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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.
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