OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials

Tracy Redden's support course.

1. A review of graphing lines, finding slope, and finding equations of lines from 2 points and a perpendicular line.

2. Review how to multiply and Factor all types of Polynomials. I cover Common Factoring, Factor by grouping, Trinomial factoring, and difference and sum of cubes!

3. I show you how to solve all types of linear equations from basic linear equations to more complicated ones with fractions and variables on both sides. There are also the ones that end up with no solutions and all reals as a solution.

4. The first step into learning how to solve a quadratic is by factoring. Here I show you how and explain why.

5. In addition we will look at the domains and restrictions of Rational Expressions.

6. How to Add and Subtract Rational Expressions. I show you how to find common denominators so you can simplify.

7. How to simplify Complex Fractions. I show you two different methods.

8. Solving quadratic equations.

... more to come soon.

When dividing polynomials of the form p(x)/(x-a) we can use synthetic division as a shortcut for polynomial long division. Below we divide using traditional polynomial long division and synthetic division side by side.

Divide.

Answer:

Both processes give the same result, x^2 - 3x - 2. However, synthetic division uses only the coefficients and requires much less writing. To understand synthetic division, we walk you through the process below. Be sure the polynomials are in standard form, that is, each term is arranged in descending order from highest power to lowest.

Step 1: Write the root a determined from (x-a) and the coefficients of the polynomial in the first line.

Step 2: Bring down the first coefficient and we are ready to begin.

Step 3: Multiply a by the first coefficient and write the result under the second coefficient.

Step 4: Add the second column and write the result below.

Step 5: Repeat the process for all of the remaining columns.

Step 6: The numbers along the bottom are the coefficients of the result in standard form beginning with a term of degree one less than the original polynomial. The last number is the remainder.

To finish, clearly present the answer to your reader. Next we do an example with a remainder. Just as we do in polynomial long division, we add a term that is the remainder over the divisor.

Divide.

Here the root (or zero) of (x+5) is -5.

Multiplying both sides by the divisor (x+5) we have the following.

We mentioned that the polynomials are required to be in standard form. Sometimes there will be "missing terms." That is, not all powers will have nonzero coefficients. In this case, we use 0 as placeholders when performing synthetic division.

Divide.