00:01
Okay, we need to find the values for the zeros of our function for h of x.
00:12
We are going to use the fact that we know there is at least one rational zero.
00:16
So to figure out what that rational zero is, we're going to use the possible rational zeros theorem.
00:21
So that says we take the factors of our constant, which is five, and we're going to put them over the factors of our leading term, which is six.
00:29
So the factors of our constant is 1 and 5.
00:33
And the factors of our leading term is 6, 3, 2, and 1.
00:37
So i'm going to call these guys my p's, these guys my q's.
00:43
So the rational root theorem says that plus or minus p over q can give us back a possible 0 of our function.
00:56
So it could be 1 over 6, it could be 1 over 3, 1 over 2, 1 over 1.
01:05
It could also be 5 over 6, 5 over 3, 5 over 2, and 5 over 1.
01:14
And it could be plus and minus all of these.
01:16
That's a lot of possibilities, right? so to figure out which one it might be, start by just substituting it back into your equation.
01:24
So ahead of time i've already done this.
01:25
So i know that when i have 5, when x equals 5, and i plug that back in, i will end up getting 0.
01:33
So that is one of my rational zeros.
01:36
And i'm going to use that five to do synthetic division with.
01:42
So when i plug that in, i get zero.
01:47
Okay.
01:51
Okay.
01:51
So since we can plug five into our function and we get back zero, it is one of our rational zeros.
01:56
So i'm going to use that five to figure out the rest of my rational zeros by using synthetic division.
02:02
So what goes inside of our box for synthetic division is all of our coefficients of our variables.
02:09
So 6, negative 31, 4, and 5.
02:18
So the first thing you do is drop that first number...