00:01
In this problem, you're given a graph of a polynomial function, and you're asked to write the polynomial in factored form.
00:08
In order to do that, we need to find the zeros, and the zeros are where we cross the x -axis.
00:15
In this case, we're crossing the x -axis in three places, at x -equals negative 1.
00:22
And since that is what we call touching the x -axis, it's going to give us an even multiplicity of 2.
00:31
Then crossing the x -axis again, this time it crosses the x -axis at x -equals 0, gives us a multiplicity of 1.
00:41
And the multiplicity just means the number of times the factor shows up, or the 0.
00:47
All right, then we end up with the last 0 at x -equals 2, and that one crosses the x -axis, so also has a multiplicity of 1.
00:59
Right, the other thing we need to know is a function, value.
01:04
So we're going to have to find where this curve gives us a nice point where it crosses.
01:09
We can use this one down here.
01:12
That one's good.
01:14
And that's a value of f of negative 2 is equal to negative 8.
01:21
You could use any point.
01:23
It looks like you could also use f of 1 equals 4.
01:28
That would also work.
01:32
All right.
01:32
So let's go ahead and write our polynomial in terms of x.
01:38
What we don't know is what this coefficient can be.
01:42
So we're going to call it an a.
01:43
We're going to put this in factored form.
01:47
And when we do that, our zeros will become the opposite sign to make the factor.
01:53
So a minus one becomes a plus one...