91Ó°ÊÓ

Use a graph and your knowledge of the zeros of polynomial functions to determine the exact values of all the solutions of each equation. $$x^{4}-4 x^{3}+5 x^{2}-4 x+4=0$$

In Exercises 11 to \(30,\) simplify and write the complex number in standard form. $$(3+\sqrt{-4})(2-\sqrt{-9})$$

Use Descartes' Rule of Signs to state the number of possible positive and negative real zeros of each polynomial function. $$P(x)=x^{3}+3 x^{2}-6 x-8$$

Determine the vertical and horizontal asymptotes and sketch the graph of the rational function \(F\). Label all intercepts and asymptotes. $$F(x)=\frac{6 x^{2}-5}{2 x^{2}+6}$$

In Exercises 11 to \(30,\) simplify and write the complex number in standard form. $$(5+2 \sqrt{-16})(1-\sqrt{-25})$$

Use a graph and your knowledge of the zeros of polynomial functions to determine the exact values of all the solutions of each equation. $$x^{4}+4 x^{3}+8 x^{2}+16 x+16=0$$

Use the Remainder Theorem to find \(P(c)\). $$P(x)=6 x^{3}-x^{2}+4 x, c=-3$$

Use the Zero Location Theorem to verify that \(P\) has a zero between \(a\) and \(b\). $$P(x)=4 x^{3}-x^{2}-6 x+1 ; a=0, b=1$$

Use Descartes' Rule of Signs to state the number of possible positive and negative real zeros of each polynomial function. $$P(x)=x^{3}-19 x-30$$

Determine the vertical and horizontal asymptotes and sketch the graph of the rational function \(F\). Label all intercepts and asymptotes. $$F(x)=\frac{x^{2}+x+4}{x^{2}+2 x-1}$$