High School Math Solutions – Polynomials Calculator, Dividing Polynomials

In the last post, we talked about how to multiply polynomials. In this post, we will talk about to divide polynomials.  When we divide polynomials, we can write these problems in the form of a fraction. This allows us to reduce the fraction and get our answer. Although this method doesn’t work every time we divide polynomials, when it does, it is a quick, simple method.

Once written in the form of a fraction, there are two ways to reduce the fraction. One method is to split the fraction up, so there is one term per fraction, having the denominator be the same. The other method is to factor the numerator and denominator and cancel out terms that are the same in the numerator and denominator.

Let’s see some examples to better understand how to solve these problems.

We will use the splitting method first for our first example.

First example (click here):

(32x^4-56x^2)\div 8x

1. Rewrite the problem in the form of a fraction

\frac{32x^4-56x^2}{8x}

2. Split the fraction

\frac{32x^4}{8x}-\frac{56x^2}{8x}

3. Reduce the fractions

\frac{8\cdot 4x^4}{8x}-\frac{8\cdot7x^2}{8x}
4x^3-7x

Next example:
We will use our same problem above, but use factoring to solve the problem.

(32x^4-56x^2)\div 8x

1. Rewrite the problem in the form of a fraction

\frac{32x^4-56x^2}{8x}

2. Factor the numerator and denominator

\frac{8x^2(4x^2-7)}{8x}

3. Cancel out common factors

4. Simplify

x(4x^2-7)
4x^3-7x

Last example (click here):

(2x^3+11x^2+5x)\div(2x^2+x)

1. Rewrite the problem in the form of a fraction

\frac{2x^3+11x^2+5x}{2x^2+x}

2. Factor the numerator and denominator

\frac{(2x+1)(x+5)x}{(2x+1)x}

3. Cancel out common factors

4. Simplify

x+5

As you can see, factoring is a big part of dividing polynomials. Before attempting these problems, make sure you’ve mastered factoring. Dividing polynomials by these two methods is pretty simple. However, these methods may not work for certain division problems. Next blog post, we will talk about another method to use, when these methods don’t work. For more practice and help on this topic, checkout Symbolab’s Practice.

Until next time,

Leah