00:01
So in this problem, we're given a graph of a polynomial function looks like this.
00:05
It says if this function has a degree of three, meaning three unique solutions, find the factored equation for f of x, which basically means that in my final answer, oops, in my final answer, i'm going to want it to look something like this with three factors because it's a degree three function.
00:26
So first let's take a look at our factors.
00:29
So i have three solutions on my polynomial function, or in this case three places where my function crosses the x -axis.
00:36
That's an x -equals negative 2, x -equals positive 2, and x -equals 5.
00:42
So those factors came from setting this function and the factors in that function equal to 0.
00:50
So if i made each of these factors, x equals negative 2, x -equals 2, and x -equals 5, and made them so they were, then set equal to zero, i would do so by adding two on both sides, giving me x plus two equals zero.
01:06
So that's one of my factors, x plus two.
01:09
I'd do the same thing here by subtracting two on both sides.
01:12
X minus two equals zero.
01:15
So x minus two is another factor.
01:17
And x equals five, i'd subtract five on both sides, giving me x minus five as another factor.
01:23
Okay.
01:24
So that's kind of the basic factored form of my equation.
01:27
But there's a couple other things i need to take into account.
01:29
First of all, this function is pointing down on the right hand side, which means that the leading coefficient has to be negative.
01:37
So this first term, whatever it is, needs to be negative...