00:01
In this question, they ask us how many x -intercepts appear on the graph of this polynomial function.
00:06
So if you want to find x -intercepts, what do you do? you set your y equal to 0, or you set your f of x equal to 0.
00:17
So we are going to be solving the equation this time, 0 equals x to the 4th minus x cubed plus x squared minus x.
00:27
And the idea is i have to factor on that right -hand side.
00:32
I first notice there is a greatest common factor.
00:35
My greatest common factor is x.
00:40
When i factor that out, i'm left with x cubed minus x squared plus x minus 1.
00:48
Now, inside those parentheses, i'm going to factor by grouping.
00:53
I look at the first two terms, and i see that my greatest common factor is x squared.
00:58
If i factor out that x squared, i'm going to be left with the quantity of x minus 1.
01:08
Now, if i look at my second two terms, my greatest common factor would just be positive 1.
01:16
And so, if you put that positive 1 out front, you're left with just the x minus 1 in parentheses.
01:24
Notice, i do have x minus 1 in both of these places as a greatest common factor.
01:31
Factor...