91Ó°ÊÓ

Examine the leading term and determine the far-left and far-right behavior of the graph of the polynomial function. $$P(x)=5 x^{5}-4 x^{3}-17 x^{2}+2$$

Use long division to divide the first polynomial by the second. $$x^{4}+3 x^{3}-5 x+3 x^{2}-1, x-4$$

Use the given zero to find the remaining zeros of each polynomial function. $$P(x)=2 x^{3}-5 x^{2}+6 x-2 ; 1+i$$

Use synthetic division to divide the first polynomial by the second. $$5 x^{3}+6 x^{2}-8 x+1, \quad x-5$$

Use a graphing utility to graph each polynomial. Use the maximum and minimum features of the graphing utility to estimate, to the nearest tenth, the coordinates of the points where \(P(x)\) has a relative maximum or a relative minimum. For each point, indicate whether the \(y\) value is a relative maximum or a relative minimum. The number in parentheses to the right of the polynomial is the total number of relative maxima and minima. $$P(x)=x^{3}+4 x^{2}-4 x-16$$

Determine the vertical and horizontal asymptotes and sketch the graph of the rational function \(F\). Label all intercepts and asymptotes. $$F(x)=\frac{x+4}{2-x}$$

Use a graphing utility to graph each polynomial. Use the maximum and minimum features of the graphing utility to estimate, to the nearest tenth, the coordinates of the points where \(P(x)\) has a relative maximum or a relative minimum. For each point, indicate whether the \(y\) value is a relative maximum or a relative minimum. The number in parentheses to the right of the polynomial is the total number of relative maxima and minima. $$P(x)=x^{3}-3 x^{2}-24 x+3$$

Use a graphing utility to graph each polynomial. Use the maximum and minimum features of the graphing utility to estimate, to the nearest tenth, the coordinates of the points where \(P(x)\) has a relative maximum or a relative minimum. For each point, indicate whether the \(y\) value is a relative maximum or a relative minimum. The number in parentheses to the right of the polynomial is the total number of relative maxima and minima. $$P(x)=-2 x^{3}-3 x^{2}+12 x+1$$

Find a polynomial function of lowest degree with integer coefficients that has the given zeros. $$3,2 i,-2 i$$

Determine the \(x\) -intercepts of the graph of \(P\). For each \(x\) -intercept, use the Even and Odd Powers of \((x-c)\) Theorem to determine whether the graph of \(P\) crosses the \(x\) -axis or intersects but does not cross the \(x\) -axis. $$P(x)=(x+2)^{3}(x-6)^{10}$$