00:01
These problems are asking us about the multiplicity of zeros and how they affect the graph of polynomial functions, and we want to select the correct drop downs to complete the statements.
00:08
So the zeros of a ninth degree polynomial function are 1 with the multiplicity of 3, 2, 4, and 6 with a multiplicity of 4.
00:18
So the multiplicity being other than 1 is very important because if the multiplicity is 1, then it just goes straight through.
00:25
If the multiplicity is an odd value higher than 1, it still goes through, but it currently, curves through.
00:31
So since this is multiplicity of three, it'll kind of show a curved cubic type of behavior when you're looking at it if you zoom in on the calculator or get close with the graph.
00:39
For the multiplicity that is even, that will touch or bounce and then turn back the other direction.
00:44
So at that six, we're going to have an image of the graph hitting that point and then turning back around from whichever direction is approaching it.
00:52
The first statement says the graph of the function will cross through the x -axis at it will cross through one, the multiplicity of three, even though it crosses through in a kind of curve behavior.
01:03
But it also crosses through at two and at four, because they didn't specify that multiplicity, so we have to assume that that's a multiplicity of one.
01:12
So i believe this should be three, because it will cross through all three of those zeros...