00:01
So f of x is a polynomial and it's 2x cubed minus 9x squared minus 38x plus 21.
00:19
I want to list all the possible rational zeros.
00:28
So to do that i'm going to use my rational zeros theorem.
00:32
I have 1, 3, 7, and 21 which are the factors of 21 over the factors of 2.
00:41
That's going to give me plus or minus 1, 3, 7, and 21 over a half, three halves, seven halves, and 21 halves.
00:58
Now i want to factor f of x completely.
01:05
So i'm going to put my function into my calculator and then i'm going to test my zeros to find the actual zeros.
01:23
So 1 and negative 1 don't work, negative 3 works, i know f of negative 3 is 0, 7 works, negative 7 doesn't work, neither 21 or negative 21 works, and a half works.
01:51
Once i find three zeros i can stop.
01:54
So i know that this polynomial is going to factor...