00:01
So the first thing we want to do is factor out this polynomial to figure out our zeros.
00:07
So if you factor out an x cubed here, what we're left with is x squared minus 9.
00:14
And so if we use difference of squares here, this can be converted to to x plus 3 and x minus 3.
00:24
So now we know that our zeros are 0, and this has a multiplicity of 3.
00:30
Notice that x cubed.
00:31
And we have negative 3 and positive 3.
00:36
And both of these have a multiplicity of 1.
00:38
So now let's look at our boundaries.
00:40
Well, as x tends to positive infinity, as x tends to positive infinity, well, we have positive infinity cubed times positive infinity times positive infinity.
00:49
And so this means our polynomial would tend to positive infinity.
00:54
And so now let's look at our other boundary, negative infinity.
00:58
And so we have negative infinity cubed is negative...