91Ó°ÊÓ

In Exercises \(11-18\), state the quotient and remainder when the first polynomial is divided by the second. Check your division by calculating (Divisor)(Quotient) + Remainder. $$3 x^{4}+8 x^{2}-6 x+1 ; \quad x+1$$

In Exercises \(1-54,\) perform the indicated operation and write the result in the form \(a+b i\). $$(0-6 i)(5+0 i)$$

Solve the inequality and express your answer in interval notation. $$-4 \leq 7-3 x < 0$$

List the roots of the polynomial and state the multiplicity of each root. $$k(x)=(x-\sqrt{7})^{7}(x-\sqrt{5})^{5}(2 x-1)$$

In Exercises \(1-54,\) perform the indicated operation and write the result in the form \(a+b i\). $$(4+3 i)(4-3 i)$$

State the quotient and remainder when the first polynomial is divided by the second. Check your division by calculating (Divisor)(Quotient) + Remainder. $$x^{5}-x^{3}+x-5 ; \quad x-2$$

Directions: When asked to find the roots of a polynomial, find exact roots whenever possible and approximate the other roots. In Exercises \(1-15,\) find all the rational mots of the polynomial. $$\frac{1}{3} x^{7}-\frac{1}{2} x^{6}-\frac{1}{6} x^{5}+\frac{1}{6} x^{4}$$

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

Find all the roots of \(f(x)\) in the complex number system; then write \(f(x)\) as a product of linear factors. $$f(x)=x^{2}-2 x+5$$

In Exercises \(1-54,\) perform the indicated operation and write the result in the form \(a+b i\). $$(2-5 i)^{2}$$