00:02
So we have a polynomial 6x cubed plus mx squared plus nx minus 5.
00:12
And this has a factor of x plus 1, which means it divides into it evenly.
00:22
But when divided by x minus 1, the remainder is negative 4.
00:29
So let's see what happens if we actually divide.
00:31
So we know that x plus 1 is a factor.
00:35
So let's use synthetic division here.
00:39
So let me just list out the coefficients.
00:45
So we know the remainder has to be zero because x plus 1 is a factor.
00:54
So let's go through synthetic division.
00:56
So we're going to bring down the 6.
00:58
Negative 1 times 6 is negative 6.
01:02
M and negative 6 would give m minus 6.
01:09
Negative 1 times m minus 6 is negative m plus 6.
01:16
Adding that to the n, we get n minus m plus 6.
01:23
And negative 1 times n minus m plus 6 would be negative n plus m minus 6.
01:31
Now in order to add to get a remainder of zero, this here must equal five.
01:41
Because negative 5 plus 5 would give us 0.
01:44
So we know that negative n plus m minus 6 has to give us 5.
01:52
So let's save that.
01:55
Now something else that we know is if we divide by x minus 1, we get a remainder of negative 4.
02:02
So let's do division by x minus 1.
02:06
So we'll put a 1 on the outside...