00:01
Okay, so here's the function we have, the polynomial we have.
00:03
We know that there's at least two rational roots, so we've got to find those first using the rational root theorem.
00:10
So remember the rational root theorem, you find all the factors of p, which are the factors of the four, so plus or minus one, two, and four, and then all the factors of q, which are plus and minus one, three, and nine, and then we're going to start with, we're going to start trying with synthetic division to find the zeros.
00:39
This is always tough, but we're going to do it.
00:43
So i'm going to start with one, right, one over one, so our possible zeros over here are plus and minus, so here's my big bracket, so one over one is one, one over three is one third, one over nine.
01:00
Then i do the two, two over one is two, two over three is two thirds, and two over nine.
01:08
And then i do it with the four, four over one is four, four over three is four thirds, and four over nine.
01:16
So there's all my possible zeros.
01:19
I'm not going to try a fraction first, and remember it's plus or minus, so i'm going to start with one, because it's one.
01:26
If that doesn't work, i'll try negative one, and then i'll go to two, and then i'll try negative two.
01:31
All right, here we go, synthetic division.
01:33
So here's a nine, here's a negative 30, 37, negative 20, and four.
01:41
All right, the exponents don't skip.
01:44
It goes x to the fourth, then x to the third, x squared, x to the first.
01:47
If it skipped, like if it went x to the fourth, and then an x squared, we'd have to put a zero in for x squared there.
01:58
Okay, so the first thing you do, bring down the nine.
02:02
One times nine is nine.
02:04
Add those together, we have negative 21.
02:08
One times negative 21 is negative 21.
02:11
Add straight down, that's 16.
02:14
One times 16 is going to be positive 16.
02:18
I think we got lucky on our first guess.
02:21
16.
02:22
One times 16 is 16.
02:24
Add that down, it's negative four.
02:27
One times negative four is negative four.
02:29
That is a zero.
02:31
So we know one of the roots, one of them, is x equals one.
02:38
All right, now we have the nine, the negative 21, the 16, and the negative four.
02:45
Nine and four are still the p and q, so it's the same possible zeros.
02:57
We could have one again.
03:00
We could try it.
03:02
Let's try it again.
03:03
If i tried one again, now i'm not going back to the original.
03:07
I'm starting with these new coefficients.
03:09
Bring down the nine.
03:11
One times nine is nine.
03:13
That adds up to a negative 12...