00:01
This is a multi -step item or three -part item.
00:06
The first part asks that we list all the possible rational zeros.
00:11
So that's part a.
00:13
So, of course, we need the factors of the final coefficient, the final constant and divided by the factors of the leading coefficient.
00:25
So the factors of six, we've got one, two, two, three, six, the factors of two, of course, we've got one and two.
00:39
Let's assemble those into a more thorough list, and then all over the two.
00:58
So now when we compile these, i'm going to use some color just to distinguish them.
01:03
We've got a one, a two, three, six.
01:07
Let's get those.
01:09
One, two, three, six.
01:12
Got a one half.
01:17
We already have a one.
01:18
We've got a one and a half, three over two, and then three.
01:24
So these are positive, negative.
01:28
All these values in blue are the complete list of possible rational roots.
01:37
So now step b wants us to use synthetic division to find a possible.
01:46
Rational root.
01:48
Because of this six and the two here, i'm going to go with a three.
01:53
So let's first try negative three.
01:56
And if that doesn't work, we'll try the positive three.
02:00
So i'm going to use the two, negative three, negative 11, and six.
02:07
Those values, of course, are the coefficients of each term in descending order and the final constant.
02:14
We drop the two and we multiply.
02:18
Negative 6, and we add.
02:23
Multiply.
02:26
Let's see, we add that.
02:28
We're going to get 16, and this does not look good, does it? negative 48, and we don't even have to add this.
02:36
We know it's not going to be a 0.
02:38
That didn't work.
02:40
Let's try the positive 3.
02:43
Again, 2, negative 3, negative 11, and 6.
02:49
Maybe i should have started with the 1 and negative 1.
02:52
Let's see.
02:55
3 times 2 is 6.
02:57
We'll add 3.
03:00
3 times 3 is 9...