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Basic Algebra

Basic Algebra

Dividing Polynomials

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 5/5=1 or  x/x=1

Dividing Monomials by Monomials

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


Instead of writing y^3 we can write yyy (which means y x y x y).


Now we can divide, or reduce, the coefficients and the variables. 18 / 9 = 2 and y/ y=1, just like 7/7=1

reduce coefficients 18yyy/9y

Simplified, this looks like:

(2x1yy)/(1x1) = 2y^2/1=2y^2

Examples: Dividing Monomials by Monomials

Example 1

Divide 125x2y by 150xy2

For simplicity, we can write this as a fraction:


Now let's write the variables the long way.


Then reduce:

reducing 125xxy/150xyy

Simplified, it look like this:

(5*1*1x)/6y = 5x/6y

Example 2

Divide 64abc/8abcd

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

reducing 64abc/8abcd



Dividing Polynomials by Monomials

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.

(16x^2 + 24x)/(-4x^2)

We can rewrite this fraction as:

16x^2/-4x^2 + 24x/-4x^2

(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:

reducing 16xx/-4xx + 24x/-4xx

Simplified, it looks like this:

(4*1*1)/(-1*1*1) + (6*1)/(-1*1*1)

4/-1 + 6/-x

-4 + 6/-x

Look Out: watch your negative signs in a fraction bar. 2/-a is the same as -2/a, which is also the same as -(2/a), but it is not the same as -2/-a , which would equal 2/a .

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