# Dividing Polynomials

In this video, we are going to divide polynomials.

For example: $\frac{x^2+5x+4}{x+1}$

Factor polynomials if necessary
$\frac{(x+4)(x+1)}{x+1}$

Divide like terms
$\frac{(x+4)}{1}$

So we have
${x+4}$

## Video-Lesson Transcript

Let’s go over how to divide polynomials.

First, we have a polynomial divided by a single term.

$\dfrac{6x + 12}{3}$

We’re going to factor this first and see if we can cancel out.

$= \dfrac{6 (x + 2)}{3}$

Then cancel $3$ and $6$.

$= \dfrac{2 (x + 2)}{1}$
$= 2 (x + 2)$

Similarly, we can do the same thing if we divide by polynomial.

Let’s say we have

$\dfrac{x^2 + 5x + 4}{x + 1}$

Let’s factor this first.

$= \dfrac{(x + 4) (x + 1)}{x + 1}$

Then cancel out and we’re left with

$= x + 4$

But that’s not always the case.

$\dfrac{x^2 + 5x + 3}{x + 1}$

We can’t factor the numerator. So we definitely can’t factor and reduce.

So what we’re going to do is long division.

Let’s review long division.

${3} )\overline{\rm 542}$

The answer is $180 \dfrac{2}{3}$

Now, let’s get back and solve using long division.

${x + 1})\overline{\rm x^2 + 5x + 3}$

Since $x + 1$ is a binomial or has tow terms, it cannot go into $x^2$ alone.

So, we’ll use $x^2 + 5x$.

The question is how many times does $x + 1$ goes into $x^2 + 5x$?

The most important thing to look at is the $x$-terms, you can ignore the other numbers for now.

So, what can we multiply to $x$ to get $x^2$?

Well, it’s $x$.

Now we have to subtract and bring down the last number.

How many $x + 1$ goes into $4x + 3$?

Again, let’s just focus on the $x$.

$x + 4 - \dfrac{1}{x + 1}$

Now, let’s look at our first example.

$\dfrac{x^2 + 5x + 4}{x + 1}$

At this point, we know that the answer is

$= x + 4$

Now, let’s just divide this using long division.

${x + 1})\overline{\rm x^2 + 5x + 4}$

$= x + 4$