91Ó°ÊÓ

Fill in the blanks. A polynomial function of degree and leading coefficient \( a_n \) is a function of the form \( f(x) = a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0 (a_n \neq 0) \) where \( n \) is a ________ _________ and \( a_n, a_{n-1}, \cdots , a_1, a_0 \) are ________ numbers.

Fill in the blanks. A __________ function is a second-degree polynomial function, and its graph is called a __________.

Fill in the blanks. If the graph of a quadratic function opens upward, then its leading coefficient is ________ and the vertex of the graph is a ________.

Fill in the blanks. If the graph of a quadratic function opens downward, then its leading coefficient is ________ and the vertex of the graph is a ________.

Fill in the blanks. If a real zero of a polynomial function is of even multiplicity, then the graph of \( f \) ________ the x-axis at \( x = a \), and if it is of odd multiplicity, then the graph of \( f \) ________ the x-axis at \( x = a \).

In Exercises 5 - 8, determine whether each value of is a solution of the inequality. Inequality \( \dfrac{x + 2}{x - 4} \ge 3 \) Values (a) \( x = 5 \) (b) \( x = 4 \) (c) \( x = -\dfrac{9}{2} \) (d) \( x = \dfrac{9}{2} \)

In Exercises 11 - 26, use long division to divide. \( (x^3 + 4x^2 - 3x - 12) \div (x - 3) \)

In Exercises 21 - 24, find the zeros (if any) of the rational function. \( h(x) = 4 + \dfrac{10}{x^2 + 5} \)

In Exercises 21 - 24, find the zeros (if any) of the rational function. \( f(x) = 1 - \dfrac{2}{x - 7} \)

In Exercises 13 - 30, solve the inequality and graph the solution on the real number line. \( x^3 + 2x^2 - 4x - 8 \le 0 \)