00:01
We're given a function, and we're asked to find the rational zeros of this function using the rational zero test.
00:12
The function is f of x equals 2x to the 4th, minus 15x cubed, plus 23x squared, plus 15x, minus 25.
00:34
To apply the rational zero test, we need to find the factors of the constant term negative 25.
00:44
So these are plus or minus 1, plus or minus 5, and plus or minus 25.
00:53
And the possible factors of the leading coefficient, which is 2.
01:05
So the possible leading coefficient factors are plus or minus 1 and plus or minus 2.
01:10
And using the rational root test, we have the possible rational zeros, include all the possible ratios of constant factors to leading coefficient factors.
01:29
This includes plus or minus 1, plus or minus 5, plus or minus 25, and also all these factors divided by 2, so plus or minus 1 half, plus or minus 5 halves, and plus or minus 25 halves.
01:50
Now this is a total of 12 different possible factors.
01:54
It could take you a while to find the right one.
01:56
So i'm just going to go ahead and skip some steps.
02:04
I'm going to go ahead and find the right zero right away.
02:10
So we're going to test the possible zero five using synthetic division.
02:22
So we have five, and then we have our coefficients to negative 15, 2315, and negative 25, 5 times 2 is 10, negative 15 plus 10 is negative 5, 5 minus 25, 5 plus negative 25, 23 plus 25 is negative 25 is negative 25, 15 minus 10 is 5, 5 times 5 is 25, and negative 25 plus 5 is 0...