The final topic in polynomials is division. We will study two different approaches:
To divide a polynomial by a monomial, we split up our fraction in several smaller fractions (one for each term on the top), each having the same denominator as the original. We then simplify each fraction individually.
To divide a polynomial by a polynomial, we will use a method that is very similar to the long division you learned in elementary school. In fact, if you try a long division problem (with numbers) before learning polynomial long division you will recognize many of the steps.
Here is a simpler example:
And here is a more complicated example: