College Algebra, Chapter 4, 4.2, Section 4.2, Problem 4

Determine which of the following statements couldn't possibly be true about the polynomial function $P$?
a.) $P$ has degree 3, two local maxima, and two local minima.
b.) $P$ has degree 3, and no local maxima or minima.
c.) $P$ has degree 4, one local maximum, and no local minima.

Statement (a) is not true, since the number of local extrema should be $n-1$. where $n$ is the degree of the polynomial. In this case, the degree of the polynomial is 3 and as its local extrema should not be greater than 2.