For each of the polynomials below, state the degree and the number of nonzero terms, and select the options that describe the long-run behavior.

a) $p(x)=(x+5)(x-3)(3 x+1)$
Degree:
Number of nonzero terms:
Long-run behavior:
A. As $x$ goes to negative $\infty$, $p(x)$ goes to negative $\infty$.
B. As $x$ goes to positive $\infty$, $p(x)$ goes to positive $\infty$.
C. As $x$ goes to negative $\infty$, $p(x)$ goes to positive $\infty$.
D. As $x$ goes to positive $\infty$, $p(x)$ goes to negative $\infty$.

b) $q(x)=4.9 x^3+13 x- 3 x^{4}$
Degree:
Number of nonzero terms:
Long-run behavior:
A. As $x$ goes to negative $\infty$, $q(x)$ goes to negative $\infty$.
B. As $x$ goes to positive $\infty$, $q(x)$ goes to negative $\infty$.
C. As $x$ goes to positive $\infty$, $q(x)$ goes to positive $\infty$.
D. As $x$ goes to negative $\infty$, $q(x)$ goes to positive $\infty$.

c) $v(x)=x^2-7x^2+ 3 x^4+1$
Degree:
Number of nonzero terms:
Long-run behavior:
A. As $x$ goes to positive $\infty$, $v(x)$ goes to negative $\infty$.
B. As $x$ goes to negative $\infty$, $v(x)$ goes to negative $\infty$.
C. As $x$ goes to positive $\infty$, $v(x)$ goes to positive $\infty$.
D. As $x$ goes to negative $\infty$, $v(x)$ goes to positive $\infty$.

d) $w(x)=- 5 x^{7}$
Degree:
Number of nonzero terms:
Long-run behavior:
A. As $x$ goes to negative $\infty$, $w(x)$ goes to negative $\infty$.
B. As $x$ goes to positive $\infty$, $w(x)$ goes to negative $\infty$.
C. As $x$ goes to positive $\infty$, $w(x)$ goes to positive $\infty$.
D. As $x$ goes to negative $\infty$, $w(x)$ goes to positive $\infty$.

Hint: