91Ó°ÊÓ

Find a polynomial function of degree 3 with the given numbers as zeros. $$-2,3,5$$

For each function: a) the maximum number of real zeros that the function can have; b) the maximum number of \(x\)-intercepts that the graph of the function can have; and c) the maximum number of turning points that the graph of the function can have. $$f(x)=x^{5}-x^{2}+6$$

Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial function as constant, linear, quadratic, cubic, or quartic. $$f(x)=15 x^{2}-10+0.11 x^{4}-7 x^{3}$$

Find a polynomial function of degree 3 with the given numbers as zeros. $$-1,0,4$$

Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial function as constant, linear, quadratic, cubic, or quartic. $$f(x)=-6$$

For each function: a) the maximum number of real zeros that the function can have; b) the maximum number of \(x\)-intercepts that the graph of the function can have; and c) the maximum number of turning points that the graph of the function can have. $$f(x)=-x-x^{3}$$

Use long division to find the quotient \(Q(x)\) and the remainder \(R(x)\) when \(P(x)\) is divided by \(d(x) .\) Express \(P(x)\) in the form \(d(x) \cdot Q(x)+R(x)\) $$\begin{array}{l}P(x)=2 x^{3}-3 x^{2}+x-1 \\\d(x)=x-3\end{array}$$

Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial function as constant, linear, quadratic, cubic, or quartic. $$f(x)=2-x^{2}$$

Determine the vertical asymptotes of the graph of the function. $$f(x)=\frac{4 x}{x^{2}+10 x}$$

Suppose that a polynomial function of degree 4 with rational coefficients has the given numbers as zeros. Find the other zero( \(s\) ). $$-1, \sqrt{3}, \frac{11}{3}$$