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(male narrator) In this video,
we will look at how we can do division with monomials.
To set this up, we will first do a quick review
of how long division works,
because we will use the same exact process
to divide with polynomials.
As we divide, with long division,
we'll first take the 5 into the 26, 5 times.
Notice as we did this,
all we truly did was we just divided...
the front...numbers.
The second thing we do
is we multiply the 5 times the 5 to get 25.
What we've done here is we have multiplied...
our answer...
by the divisor.
The next thing we do is we don't actually use 25.
But we change it to -25, so we can combine:
26 and -25 is 1.
What we've truly done here is we have changed the sign...
on the 25, making it negative, and combine.
Next, we would bring down the 3 to make it 13.
We bring down...
the next...number.
Finally, what we'll do
is then we would start dividing the 5 into 13.
In other words, we're going to start repeating the process.
We divide the front numbers-- 5 into 13--twice.
We then multiply the 2 by the divisor 5 and get 10.
We change the sign on the 10 and combine to get 3.
We then bring down the next number--or 2--
and repeat the process.
We divide 5 into the 32, and it goes in there 6 times:
5 times 6 is 30... whoops, wrong color.
So multiplied by the divisor: 5 times 6 is 30.
And we change the sign and combine to get 2.
When there's nothing left to bring down,
we say that 2 is the remainder.
We use this exact same process in order to divide polynomials.
The only difference with a polynomial
is that we no longer have numbers.
Instead, we'll change the word "number" to "terms."
When we do that, we see our process is going to be
to divide the front terms...
multiply this by the divisor...
change the sign and combine...
bring down the next terms...
and repeat the process.
In the next part of this video, we will see how this works,
where we divide out a monomial from a polynomial.