00:01
All right, in this video, i'm going to be showing you how this function here, x to the third, minus 4x square, minus 3x plus 2, has a 0 at negative 1.
00:15
So again, let me just show you the graph, just to kind of show you what that looks like.
00:19
Okay, so again, this graph right here, we have negative 1 ,0, and then these other two decimals.
00:23
The one i'm kind of focusing on now on this graph is the negative 1.
00:26
Okay? i'm going to show you algebraically how that's true.
00:29
All right, there's a couple different ways you can show it.
00:31
One way is using synthetic division.
00:34
This is one way you can do it.
00:36
Essentially we do synthetic division, and this is just how i set up my problem.
00:39
I make a little half box right here, or at least call it a half box.
00:42
Put a negative one right here, and they're going to write all the coefficients to your polynomial right next to that.
00:47
So again, you're just working with the numbers.
00:48
So the coefficient first is one, because i understand one in front of the x of the third.
00:52
We have negative four, negative three, and two.
00:56
You'll leave some space between those numbers.
00:58
I just wrote down and draw fours on a line.
01:00
And then i put a vertical line between the last few numbers just to represent what the remainder will be.
01:04
Again, it's just how i set up my synthetic division.
01:05
The first thing you're going to do to work out the synthetic division is you're going to bring down the one.
01:10
And then you're just multiplying and adding all the way through.
01:13
Again, obviously, take an account for the signs.
01:16
And ultimately, if it is a zero, the remainder should be zero because the y value is zero if it's a true zero.
01:25
Okay, that's what i'm looking for.
01:27
All right, so i'm going to bring down this one.
01:28
I'm going to do one times negative one...