00:02
The topic today is dividing polynomials using long division.
00:06
And over to the left, you'll see where i have the question marks.
00:09
That's the original question.
00:10
But i want to start by just going back to basic long division, just using a three -digit number divided by a one -digit number.
00:19
So let's go over the parts before we begin.
00:22
The part that's underneath is referred to as your dividend.
00:29
Okay.
00:29
And in function terms, that's your p of x.
00:37
Then the number is being divided by, that's your divisor.
00:42
We refer to it as d of x.
00:46
The answer that we're going to get when we solve this problem is referred to as q of x or the quotient.
00:57
All right on this side.
01:02
And then whatever, if we get a remainder, it's referred to as r of x.
01:07
Let's go through our steps because they're going to be the same as the same.
01:10
Four long division with polynomials.
01:13
So i'm going to take the first digit on the inside and divide by the first digit on the outside, so 8 divided by 4 is 2.
01:23
Then i'm going to multiply 4 times 2 to get 8.
01:27
I'm going to subtract to get 0, and then i'm going to bring down.
01:35
Every time you bring down, you have to start that whole process over again until you don't have anything else to bring down.
01:42
So i brought down the one.
01:44
So i'm going to take one and divide it by four.
01:47
Well, that gives me a fraction.
01:49
I can't divide one by four evenly.
01:52
So i'll put a placeholder.
01:54
Four times zero is zero.
01:57
I'll subtract.
02:00
Bring down.
02:02
And because i brought down, i have to go again.
02:05
13 divided by 4, 3, then i'll have a remainder, but 4 times 3 is 12.
02:14
I subtract and get 1.
02:16
There's nothing left to bring down, so i know that i'm done, and what's left is referred to as my remainder.
02:24
Just kind of refer to a regular problem, division problem, and those are your parts, and those are how it's abbreviated.
02:31
So let's set up our actual polynomial division, so our p of x is going to go under underneath, so x cubed.
02:44
Now, with numbers, so for example, for our quotient, we had 203.
02:49
I had to put a zero in the tens place because i'd had no tens.
02:54
So you have to put placeholders just like you would in any other number.
02:58
So i'm going to say plus zero x squares because i have no x squared plus zero x minus 216.
03:08
You must have a placeholder.
03:12
So even though i don't have any squares or x's, i have to put a placeholder or this is not going to come out correctly.
03:19
My d of x, that's the dividend, just like with this one, it goes on the outside.
03:25
So x plus six.
03:29
And now we're set up to start dividing.
03:33
I'm going to start the exact same way.
03:35
The first term on the inside.
03:38
And in this case, i have two terms on the outside.
03:41
Going to divide the first one.
03:43
For the first time on the inside, divided by first term on the outside.
03:48
I'm going to come off to the side and write this in red.
03:51
So what i'm doing is x cubed divided by x...