[Solution Library] a. Show U(x)=x^2(x^2-25)(x+8) is a polynomial by multiplying all factors. b. What is the degree of U(x) ? c. How many terms does U(x) have? d.
Question: a. Show \(U\left( x \right)={{x}^{2}}\left( {{x}^{2}}-25 \right)\left( x+8 \right)\) is a polynomial by multiplying all factors.
b. What is the degree of \(U\left( x \right)\) ?
c. How many terms does U(x) have?
d. What are the zeros? Include any multiplicities.
e. What is the y-intercept?
f. What is the long run behavior? The graph is shaped like the leading term: y = ____ as \(x\to \infty \), U(x) \(\to \) ______ and as \(x\to -\infty \), \(U\left( x \right)\to \) _____
g. Graph U(x) on your calculator. Indicate an appropriate window: x min =____, x max = _____ y min = ____, y max = _____
h. How many turning points ("bumps" or local extrema) does this graph have?
Deliverable: Word Document 
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