A polynomial \(f\) of degree \(10\) whose zeros are \(x = -12\) (multiplicity \(3\)), \(x = -9\) (multiplicity \(2\)), \(x = 4\) (multiplicity \(4\)), and \(x = 10\) (multiplicity \(1\)), and \(f\) satisfies \(f(0) = 21\text{.}\) What can you say about the values of \(\lim_{x \to -\infty} f(x)\) and \(\lim_{x \to \infty} f(x)\text{?}\)

A polynomial \(p\) of degree \(9\) that satisfies \(p(0) = -2\) and has the graph shown in the following figure. Assume that all of the zeros of \(p\) are shown in the figure.

A polynomial \(q\) of degree \(8\) with \(3\) distinct real zeros (possibly of different multiplicities) such that \(q\) has the sign chart in the figure below and satisfies \(q(0) = -10\text{.}\)

A polynomial \(q\) of degree \(9\) with \(3\) distinct real zeros (possibly of different multiplicities) such that \(q\) satisfies the sign chart in part (c) and satisfies \(q(0) = -10\text{.}\)

A polynomial \(p\) of degree \(11\) that satisfies \(p(0) = -2\) and \(p\) has the graph shown in part (b). Assume that all of the zeros of \(p\) are shown in the figure.