91Ó°ÊÓ

Without graphing, determine the vertex of the given parabola and state whether it opens upward or downward. $$f(x)=x^{2}-5 x-7$$

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. $$x^{15}-x-1$$

Without graphing, determine the vertex of the given parabola and state whether it opens upward or downward. $$y=-4 x^{2}+8 x-1$$

In Exercises \(1-54,\) perform the indicated operation and write the result in the form \(a+b i\). $$i^{19}$$

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. $$2 x^{3}-2 x^{2}+3 x-3$$

Solve the inequality and express your answer in interval notation. $$2 x+3 \leq 5 x+6 < -3 x+7$$

State the quotient and remainder when the first polynomial is divided by the second. Check your division by calculating (Divisor)(Quotient) + Remainder. $$5 x^{4}+5 x^{2}+5 ; \quad x^{2}-x+1$$

Find all the roots of \(f(x)\) in the complex number system; then write \(f(x)\) as a product of linear factors. \(f(x)=x^{3}-27[\text { Hint: Factor first. }]\)

Use algebra to determine the location of the vertical asymptotes and holes in the graph of the function. $$f(x)=\frac{x^{2}+8 x+2}{x^{2}+7 x+2}$$

Solve the inequality and express your answer in interval notation. $$2 x-1 < x+4 < 9 x+2$$