- Topics At a Glance
- Arithmetic, Geometric & Exponential Patterns
- Algebraic Expressions
- Evaluating Algebraic Expressions
- Combining Like Terms
- Distributive Property
- Multiplying Monomials
- Multiplying Binomials
**Dividing Polynomials**- Graphing X-Y Points
- Solving One-Step Equations
- Solving Two-Step Equations
- Solving More Complex Equations
- Solving Equations with Variables on Both Sides
- Solving Funky Equations
- Graphing Inequalities
- Solving Inequalities
- Graphing Lines
- Intercepts
- Graphing Horizontal & Vertical Lines
- Graphing Lines By Plotting Points
- Slope-Intercept Form
- Solving Multiple Equations by Graphing

**Dividing polynomials** can be a very complicated task, but not to worry, you will be able to handle these well if you follow the examples below.

The most important thing to remember is that *when you divide a variable by itself, it equals one,* just like or

Let's look at an example. *Remember, fractions are just another way to write division.*

Instead of writing we can write yyy (which means ).

Now we can divide, or reduce, the coefficients and the variables. and , just like

Simplified, this looks like:

**Example 1**

Divide 125x^{2}y by 150xy^{2}

For simplicity, we can write this as a fraction:

Now let's write the variables the long way.

Then reduce:

Simplified, it look like this:

**Example 2**

Divide

There are no variables with exponents that we need to write out, so we can go straight into reducing:

Simplified:

You may also need to divide polynomials by monomials. To do this, you need to separate the "fractions" into smaller fractions with just one term in each numerator.

We can rewrite this fraction as:

(Remember, when you add fractions together you combine the numerators and keep the denominator.)

Now, let's write out the variables the long way:

Then reduce:

Simplified, it looks like this:

**Look Out**: watch your negative signs in a fraction bar. is the same as , which is also the same as , but it is not the same as , which would equal .

Example 1

Divide |

Example 2

Divide by |

Exercise 1

Divide by

Exercise 2

Simplify

Exercise 3

Divide by

Exercise 4

Simplify