5.3E: Graphs of Polynomial Functions (Exercises)

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For the following exercises, find all zeros of the polynomial function, noting multiplicities.

13. $f(x)=(x+3)^{2}(2 x-1)(x+1)^{3}$

14. $f(x)=x^{5}+4 x^{4}+4 x^{3}$

15. $f(x)=x^{3}-4 x^{2}+x-4$

For the following exercises, based on the given graph, determine the zeros of the function and note multiplicity.

16.

$Graph of an odd-degree polynomial with two turning points.$

17.

$Graph of an even-degree polynomial with two turning points.$

18.

Use the Intermediate Value Theorem to show that at least one zero lies between 2 and 3 for the function \[f(x)=x^{3}-5 x+1 \nonumber\]