91Ó°ÊÓ

In Exercises 11 to \(30,\) simplify and write the complex number in standard form. $$(3-5 i)-(8-2 i)$$

Use the Rational Zero Theorem to list possible rational zeros for each polynomial function. $$P(x)=x^{5}-x^{4}-7 x^{3}+7 x^{2}-12 x-12$$

Use synthetic division to divide the first polynomial by the second. $$x^{5}-10 x^{3}+5 x-1, x-4$$

Use the given zero to find the remaining zeros of each polynomial function. $$P(x)=x^{4}-4 x^{3}+14 x^{2}-4 x+13 ; \quad 2-3 i$$

Use the Rational Zero Theorem to list possible rational zeros for each polynomial function. $$P(x)=x^{5}-32$$

In Exercises 11 to \(30,\) simplify and write the complex number in standard form. $$(1-3 i)+(7-2 i)$$

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. $$P(x)=x^{3}+x^{2}-9 x-9$$

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

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

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. $$P(x)=x^{3}+4 x^{2}-4 x-16$$