00:01
We're going to solve this division problem here on the left using the synthetic method, and we're going to provide it in the answer form here on the top right.
00:10
So first of all, this problem is a little different from a regular division problem using polynomials because we are using, first of all, we're using synthetic division, and synthetic division is really, really dependent on the terms.
00:26
If you notice in this dividend, we have x cubed, x squared, and then it jumps straight into a constant.
00:37
But we need that extra x in order for synthetic division to work.
00:42
So in order to solve this, you need to put what's called a placeholder.
00:52
And we're basically going to rewrite the problem so that synthetic division can work.
00:58
So we can do this x cubed minus 3x squared plus 0x minus 37.
01:08
That is our new dividend in order to solve for synthetic division.
01:13
And we're going to divide that for x minus 5.
01:17
And again, well, this is our placeholder.
01:24
So now we can start solving synthetically, just like normal.
01:28
First, we need to zero our divisor.
01:33
In this case, our divisor is x minus 5, and we need to equal that to 0, and we can get x by itself by adding 5 to both side.
01:42
And we get x equals 5.
01:45
Next, we can set up and solve the problem.
01:52
So on the outside, our 0 .0 divisor would be there.
01:58
So this is 5.
02:00
And then now we can take the terms of our new dividend and place them on the inside.
02:07
So we have 1, negative 3, 0, which that's our placeholder, and negative 37.
02:17
Now we can just, we can start the process of solving synthetically.
02:22
First thing to do, of course, is to drop down the leading coefficient, which is this case is 1.
02:28
And we can start to do the process of multiplying our resultant with our divisor and then placing it in the next column...