00:01
Hello, hope you're doing well.
00:02
So we have our function f of x here.
00:04
We have our k value right here.
00:07
So essentially, in order to write f of x in the form that the problem asks this to, you're essentially going to use synthetic division to divide our f of x function, divide this by x minus k, where k is equal to minus 4.
00:27
So x minus minus 4 will be x plus 4.
00:30
So this is essentially the synthetic division problem that we're solving.
00:33
So we'll keep this in mind for later.
00:35
So now we're going to set up our synthetic divisions.
00:39
We're going to write all of the coefficients of our f -of -x function down.
00:43
So we have 2, 3, minus 16, and 10.
00:52
And then we've got k is equal to minus 4.
00:55
So we're putting that on the outside.
00:58
So then using synthetic division to divide this, you can bring down this 2 here.
01:05
We've got 2 times minus 4, which gives us minus 8.
01:07
3 minus 8 gives us minus 5.
01:10
Minus 5 times minus 4 gives us 20.
01:13
Minus 16 plus 20 gives us 4.
01:15
4 times minus 4 gives us minus 16.
01:18
10 minus 16 gives us minus 6.
01:21
So we're left with...
01:23
So this is what we're left with.
01:25
So this is our remainder value here.
01:27
This is our constant or x to the zero value.
01:30
This is our x value...