91Ó°ÊÓ

MODELING WITH MATHEMATICS From 1890 to 2000 the American Indian, Eskimo, and Aleut population \(P\) (in thousands) can be modeled by the function \(P=0.004 t^3-0.24 t^2+4.9 t+243\), where \(t\) is the number of years since 1890 . In which year did the population first reach 722,000?

In Exercises 43–48, use Pascal’s Triangle to expand the binomial. \((2 t+4)^3\)

Find the zero(s) of the function. $$ h(x)=4 x^2+36 $$

THOUGHT PROVOKING Write an even degree polynomial function such that the end behavior of \(f\) is given by \(f(x) \rightarrow-\infty\) as \(x \rightarrow-\infty\) and \(f(x) \rightarrow-\infty\) as \(x \rightarrow \infty\). Justify your answer by drawing the graph of your function.

Determine whether the binomial is a factor of the polynomial function. $$ t(x)=48 x^4+36 x^3-138 x^2-36 x ; x+2 $$

Determine whether the function is even, odd, or neither. $$f(x)=-x^3+2 x-9$$

Write a polynomial function f of least degree that has a leading coefficient of 1 and the given zeros. \(4,6-\sqrt{7}\)

MODELING WITH MATHEMATICS Over a period of 14 years, the number \(N\) of inland lakes infested with zebra mussels in a certain state can be modeled by $$ N=-0.0284 t^4+0.5937 t^3-2.464 t^2+8.33 t-2.5 $$ where \(t\) is time (in years). In which year did the number of infested inland lakes first reach 120 ?

In Exercises 43–48, use Pascal’s Triangle to expand the binomial. \((2 q-3)^4\)

Show that the binomial is a factor of the polynomial. Then factor the function completely. $$ g(x)=x^3-x^2-20 x ; x+4 $$