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Study Guide

**Dividing polynomials** starts with dividing monomials, and dividing monomials boils down to reducing fractions, and reducing fractions? Pshaw, we've been doing that for eons. No big whoop. The fractions have variables now, but so what? We've got this.

The most important thing to remember is that when we divide a variable by itself, it equals 1, just like 5 ÷ 5 = 1 or *x* ÷ *x* = 1.

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:

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

Divide .

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

Simplify that beast.

We may also need to divide polynomials by monomials. To do this, we 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's not the same as , which would equal .

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