91Ó°ÊÓ

Use synthetic division to divide the first polynomial by the second. $$x^{4}+1, \quad x+1$$

Find the smallest positive integer and the largest negative integer that, by the Upper-and Lower-Bound Theorem, are upper and lower bounds for the real zeros of each polynomial function. $$P(x)=x^{3}-19 x-28$$

In Exercises 11 to \(30,\) simplify and write the complex number in standard form. $$(5-3 i)-(2+9 i)$$

Use the given zero to find the remaining zeros of each polynomial function. $$P(x)=x^{5}-x^{4}-4 x^{3}-4 x^{2}-5 x-3 ; \quad i$$

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

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. $$P(x)=x^{4}-4 x^{3}-2 x^{2}+12 x-5$$

Use synthetic division to divide the first polynomial by the second. $$8 x^{3}-4 x^{2}+6 x-3, x-\frac{1}{2}$$

Find the smallest positive integer and the largest negative integer that, by the Upper-and Lower-Bound Theorem, are upper and lower bounds for the real zeros of each polynomial function. $$P(x)=2 x^{3}+x^{2}-25 x+10$$

Determine the vertical and horizontal asymptotes and sketch the graph of the rational function \(F\). Label all intercepts and asymptotes. $$F(x)=\frac{1}{x^{2}-9}$$

Use the given zero to find the remaining zeros of each polynomial function. $$P(x)=x^{5}-3 x^{4}+7 x^{3}-13 x^{2}+12 x-4 ;-2 i$$