Activity 5.2.3.
Consider the polynomial function given by
\begin{equation*}
p(x) = 4692(x+1520)(x^2+10000)(x-3471)^2(x-9738)\text{.}
\end{equation*}
(a)
What is the degree of \(p\text{?}\) How can you tell without fully expanding the factored form of the function?
(b)
What can you say about the sign of the factor \((x^2 + 10000)\text{?}\)
(c)
What are the zeros of the polynomial \(p\text{?}\)
(d)
Construct a sign chart for \(p\) by using the zeros you identified in (c) and then analyzing the sign of each factor of \(p\text{.}\)
(e)
Without using a graphing utility, construct an approximate graph of \(p\) that has the zeros of \(p\) carefully labeled on the \(x\)-axis.
(f)
Use a graphing utility to check your earlier work. What is challenging or misleading when using technology to graph \(p\text{?}\)
