In this video, we are going to divide polynomials. After you finish this lesson, view all of our Algebra 1 lessons and practice problems.
Factor polynomials if necessary
Divide like terms
So we have
Let’s go over how to divide polynomials.
First, we have a polynomial divided by a single term.
We’re going to factor this first and see if we can cancel out.
Then cancel and .
Similarly, we can do the same thing if we divide by polynomial.
Let’s say we have
Let’s factor this first.
Then cancel out and we’re left with
But that’s not always the case.
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.
The answer is
Now, let’s get back and solve using long division.
Since is a binomial or has tow terms, it cannot go into alone.
So, we’ll use .
The question is how many times does goes into ?
The most important thing to look at is the -terms, you can ignore the other numbers for now.
So, what can we multiply to to get ?
Well, it’s .
Now we have to subtract and bring down the last number.
How many goes into ?
Again, let’s just focus on the .
So our final answer is
Now, let’s look at our first example.
At this point, we know that the answer is
Now, let’s just divide this using long division.
The answer is
Just like when we factored and reduced.