91Ó°ÊÓ

In Exercises \(16-22,\) factor the polynomial as a product of lin. ear factors and a factor \(g(x)\) such that \(g(x)\) is either a constant or a polynomial that has no rational roots. $$x^{6}-4 x^{5}+3 x^{4}-12 x^{3}$$

Find the horizontal asymptote, if any, of the graph of the given function. If there is a horizontal asymptote, find a viewing window in which the ends of the graph are within .1 of this asymptote. $$g(x)=\frac{3 x^{5}+2 x^{4}+1}{6 x^{5}+8 x^{4}-3 x^{2}+2 x+1}$$

Determine whether the first polynomial is a factor of the second. $$x^{2}+9 ; \quad 4 x^{5}+13 x^{4}+36 x^{3}+108 x^{2}-81$$

In Exercises \(16-22,\) factor the polynomial as a product of lin. ear factors and a factor \(g(x)\) such that \(g(x)\) is either a constant or a polynomial that has no rational roots. $$x^{5}-2 x^{4}+2 x^{3}-3 x+2$$

Find all the roots of \(f(x)\) in the complex number system; then write \(f(x)\) as a product of linear factors. $$f(x)=x^{6}-64$$

In Exercises \(1-54,\) perform the indicated operation and write the result in the form \(a+b i\). $$(-i)^{53}$$

Solve the inequality and express your answer in interval notation. $$2 x+5 \leq 4-3 x < 1-4 x$$

Without graphing, determine the vertex of the given parabola and state whether it opens upward or downward. $$g(x)=-x^{2}-6 x+4$$

Find all the roots of \(f(x)\) in the complex number system; then write \(f(x)\) as a product of linear factors. $$f(x)=x^{4}-1$$

\(a, b, c,\) and \(d\) are positive constants. Solve the inequality for \(x .\) $$a x-b < c$$