# Rewrite Rational Expressions (Synthetic Division)

Videos and lessons to 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.

### 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

Related Topics:
Polynomial Long Division

Common Core (Algebra)

Common Core for Mathematics

Synthetic Division
Synthetic division is a method of performing polynomial long division, with less writing and fewer calculations. Also, the subtractions in long division are converted to additions by switching the signs at the very beginning, preventing sign errors. The method of Synthetic Division shown in this lesson is used for division by binomials of the form (x - a).

Basic algorithm for Synthetic Division.
Synthetic Division Example 2
Another example of applying the basic synthetic division algorithm.

Why Synthetic Division Works
Demonstrating why synthetic division gives you the same result as traditional algebraic long division.
Polynomial Division: Synthetic Division.

Ex 1: Divide a Trinomial by a Binomial Using Synthetic Division
This video provides two basic examples of dividing degree two trinomials by degree one binomials.
Ex 2: Divide a Polynomial by a Binomial Using Synthetic Division
This video provides an example of dividing a polynomial by a binomial. There are no missing terms in the dividend. There is a remainder.

Ex 3: Divide a Polynomial by a Binomial Using Synthetic Division
This video provides an example of dividing a polynomial by a binomial. There are missing terms in the dividend. There is a remainder.
Ex 4: Divide a Polynomial by a Binomial Using Synthetic Division
This video provides an example of dividing a polynomial by a binomial. There are missing terms in the dividend. There is no remainder.

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