91Ó°ÊÓ

Find the degree, the leading term, the leading coefficient, the constant term and the end behavior of the given polynomial. \(f(x)=\sqrt{3} x^{17}+22.5 x^{10}-\pi x^{7}+\frac{1}{3}\)

In Exercises 7 - 20 use synthetic division to perform the indicated division. Write the polynomial in the form \(p(x)=d(x) q(x)+r(x)\). \(\left(3 x^{2}-2 x+1\right) \div(x-1)\)

Find the real zeros of the given polynomial and their corresponding multiplicities. Use this information along with a sign chart to provide a rough sketch of the graph of the polynomial. Compare your answer with the result from a graphing utility. \(g(x)=(2 x+1)^{2}(x-3)\)

Find the real zeros of the polynomial using the techniques specified by your instructor. State the multiplicity of each real zero. \(f(x)=x^{3}+4 x^{2}-11 x+6\)

Find the real zeros of the given polynomial and their corresponding multiplicities. Use this information along with a sign chart to provide a rough sketch of the graph of the polynomial. Compare your answer with the result from a graphing utility. \(P(x)=(x-1)(x-2)(x-3)(x-4)\)

In Exercises 21-30, determine \(p(c)\) using the Remainder Theorem for the given polynomial functions and value of \(c\). If \(p(c)=0,\) factor \(p(x)=(x-c) q(x)\). \(p(x)=2 x^{2}-x+1, c=4\)

Find the real zeros of the polynomial using the techniques specified by your instructor. State the multiplicity of each real zero. \(f(x)=x^{4}+2 x^{2}-15\)

Find the real zeros of the polynomial using the techniques specified by your instructor. State the multiplicity of each real zero. \(f(x)=3 x^{4}-14 x^{2}-5\)

Solve the polynomial inequality and state your answer using interval notation. \(x^{4}-9 x^{2} \leq 4 x-12\)

Solve the polynomial inequality and state your answer using interval notation. \(3 x^{2}+2 x