00:01
This is a multi -part item.
00:03
In the first prompt asks you to list all the possible rational roots for this given function, a given equation.
00:14
So recall that to do that, we're going to be listing the factors of the final constant and divided by the factors of the leading term coefficient.
00:23
So the leading term coefficient is one.
00:26
So that's nice and easy.
00:27
Leading a factors of four, positive negative 1, 2, and 4.
00:36
So the final list here of possible rational roots is 1, 2.
00:44
That's your answer.
00:47
Okay.
00:48
Part b asks us to use this list of 6 possible rational roots and actually find one using synthetic division.
00:57
So let's start off with 1.
01:00
Let's see if one works.
01:02
Set up 1, negative 2, negative 5, 8, and 4.
01:12
We drop the 1, multiply, and then add.
01:17
We multiply, and then add.
01:21
Multiply, add, and then add.
01:25
Multiply, add, and we did not find a 0.
01:32
Let's try 2.
01:33
Set this up again.
01:45
Drop the 1.
01:45
1, multiply by 2.
01:50
Multiply by 2, add, multiply by 2, add, multiply by 2, add, multiply by 2, and we found a 0, or a root.
02:05
So we know that one of the roots is x equals 2.
02:11
Okay, so now we're going to use that root, and we're not going to use that root.
02:17
I apologize, we're going to use the quotient, this result here, and we are going to find, the other rational the other roots we're going to solve the equation so we've got x cubed minus 5x minus 2 equals zero so and this is part c we need to get a little creative here because this isn't factorable in this form at least not that i recognize it's factorable so i'm going to i'm going to try synthetic division again.
03:00
And this time i'm going to try the negatives.
03:02
Let's see what we can find.
03:04
I'll go to 1 .0 for the square term, negative 5, negative 2.
03:16
1, negative 1.
03:19
Add, multiply, multiply...