00:01
This is a three -part item.
00:04
The first part wants you to list all possible rational roots.
00:09
So we list them as positive negative.
00:13
One, the factors of one, the final constant, divided by the factors of two, the leading term coefficient.
00:23
So the list here of all possible rational zeros is 1 over 1 or 1 over 2.
00:33
So finally, one or one half.
00:38
This is your list of possible rational roots.
00:41
Of course, very important.
00:43
I almost forgot.
00:45
Positive, negative.
00:48
Okay, so that takes care of item a.
00:53
B is asking that you use this list to find one of the actual zeros of the function.
01:01
So let's start off by using one.
01:03
We write 2, 1, negative 3, and 1.
01:13
These are all the coefficients of the terms in descending order.
01:18
Order of degree.
01:20
We drop the 2, multiply by 1, and add.
01:25
Multiply by 1, add, multiply by 1, add.
01:35
So we have not found a 0 yet.
01:38
Let's try negative 1.
01:39
Let's drop the 2.
01:48
Negative 1 times 2.
01:51
It's negative 2.
01:53
We add negative 1.
01:55
Multiply.
01:57
We get 1.
01:58
We add.
02:00
Multiply.
02:01
We get 2.
02:03
We add.
02:04
We still have not found an actual 0.
02:12
Let's try 1 half.
02:18
2 .1.
02:20
Negative 3.
02:22
1.
02:27
Let's drop the 2.
02:28
Multiply by a half we get one we add we get a two we multiply by a half we get one we add we get a negative two we multiply by the half we get negative one we add and we get zero and we have found one of our zeros so we can begin to populate our list with positive one half we're going to take this result we've got to a 2 -2 -2 -2...