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Dividing Polynomials

In this video, we are going to divide polynomials.

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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}

Dividing Polynomials

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.

So our final answer is

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}

The answer is

= x + 4

Just like when we factored and reduced.