91Ó°ÊÓ

The _____ _____ of _____ states that if \(f(x)\) is a polynomial of degree \(n(n>0),\) then \(f\) has at least one zero in the complex number system.

A polynomial function of \(x\) with degree \(n\) has the form \(f(x)=a_{n} x^{n}+a_{n-1} x^{n-1}+\ldots+a_{1} x+a_{0}\) \(\left(a_{n} \neq 0\right),\) where \(n\) is a _____ _____ and \(a_{n}, a_{n-1}, \ldots, a_{1}, a_{0}\) are _____ numbers.

The ______ is used to determine the left-hand and right-hand behavior of the graph of a polynomial function.

When a real zero of a polynomial function is of even multiplicity, the graph of \(f\) ______ the \(x\) -axis at \(x=a,\) and when it is of odd multiplicity, the graph of \(f\) ______ the \(x\) -axis at \(x=a.\)

When the graph of a quadratic function opens downward, its leading coefficient is ________ and the vertex of the graph is a ________.

A polynomial function is written in _________ form when its terms are written in descending order of exponents from left to right.

Use long division to verify that \(y_{1}=y_{2}.\) $$y_{1}=\frac{x^{4}-3 x^{2}-1}{x^{2}+5}, \quad y_{2}=x^{2}-8+\frac{39}{x^{2}+5}$$

Solve the inequality. Then graph the solution set. $$x^{2} \leq 16$$

Apply the Leading Coefficient Test Describe the right-hand and left-hand behavior of the graph of the polynomial function. $$f(x)=2 x^{2}-3 x+1$$

(a) state the domain of the function, (b) identify all intercepts, (c) find any vertical or horizontal asymptotes, and (d) plot additional solution points as needed to sketch the graph of the rational function. $$g(x)=\frac{1}{6-x}$$