Exam 3: Polynomial and Rational Functions

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. - $2 x ^ { 2 } + 5 x - 12 \leq 0$

Solve the problem. -You have 184 feet of fencing to enclose a rectangular region. What is the maximum area?

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. - $4 x ^ { 2 } < 3 x + 1$

Use the Rational Zero Theorem to list all possible rational zeros for the given function. - $f ( x ) = x ^ { 5 } - 3 x ^ { 2 } + 4 x + 7$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = ( x + 4 ) ^ { 2 } - 2$

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. - $x ^ { 3 } - 8 x ^ { 2 } - x + 8 = 0$

Determine the constant of variation for the stated condition. -The amount of paint needed to cover the walls of a room varies jointly as the perimeter of the room and the height of the wall. If a room with a perimeter of 70 feet and 10 -foot walls requires 7 quarts of paint, find the amount of paint needed to cover the walls of a room with a perimeter of 55 feet and 8 -foot walls.

Divide using long division. - $\frac { x ^ { 4 } + 5 x ^ { 3 } + 7 x ^ { 2 } - 3 x - 30 } { x ^ { 2 } + 4 x + 5 }$

Graph the polynomial function. -

Find the indicated intercept(s) of the graph of the function. - $y$ -intercept of $f ( x ) = \frac { x ^ { 2 } - 8 x } { x ^ { 2 } + 6 x - 15 }$

Solve Problems Involving Joint Variation -r varies jointly as $y$ and the difference between $p$ and $h$ .

Find the y-intercept of the polynomial function. -

Solve the problem. -An arrow is fired straight up from the ground with an initial velocity of 240 feet per second. Its height, $\mathrm { s } ( \mathrm { t } )$ , in feet at any time $t$ is given by the function $s ( t ) = - 16 t ^ { 2 } + 240 t$ . Find the interval of time for which the height of the arrow is greater than 116 feet.

Graph the rational function. -

Divide using long division. -A rectangle with width $2 x + 3$ inches has an area of $2 x ^ { 4 } + 9 x ^ { 3 } - 11 x ^ { 2 } - 78 x - 72$ square inches. Write a polynomial that represents its length.

Find the y-intercept of the polynomial function. - $f ( x ) = ( x + 1 ) ( x - 5 ) ( x - 1 ) ^ { 2 }$

Write an equation that expresses the relationship. Use k as the constant of variation. - $y = 4$ when $x = \frac { 1 } { 2 }$

Write an equation that expresses the relationship. Use k as the constant of variation. -When the temperature stays the same, the volume of a gas is inversely proportional to the pressure of the gas. If a balloon is filled with 60 cubic inches of a gas at a pressure of 14 pounds per square inch, find the new pressure of the gas if the volume is decreased to 12 cubic inches.

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers. - $f ( x ) = 9 x ^ { 5 } + 6 x ^ { 3 } - 4 x ^ { 2 } + 1$ ; between $- 1$ and 0

Find the y-intercept of the polynomial function. - $f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 24 x + 20$