91Ó°ÊÓ

Use synthetic division to divide the first polynomial by the second. $$6 x^{4}-2 x^{3}-3 x^{2}-x, x-5$$

In Exercises 11 to \(30,\) simplify and write the complex number in standard form. $$(2-6 i)+(4-7 i)$$

Use the Rational Zero Theorem to list possible rational zeros for each polynomial function. $$P(x)=x^{4}-1$$

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. $$P(x)=x^{3}-3 x^{2}-24 x+3$$

In Exercises 11 to \(30,\) simplify and write the complex number in standard form. $$(-3-5 i)-(7-5 i)$$

Use the given zero to find the remaining zeros of each polynomial function. $$P(x)=x^{4}-4 x^{3}+19 x^{2}-30 x+50 ; 1+3 i$$

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

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

Determine the vertical and horizontal asymptotes and sketch the graph of the rational function \(F\). Label all intercepts and asymptotes. $$F(x)=\frac{x+3}{1-x}$$

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. $$P(x)=x^{3}-19 x-28$$