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**

Polynomial Long Division

Common Core Algebra

Common Core Mathematics

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

**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.

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.