RESISTORS When two resistors of resistances and are

Between two consecutive zeros, a polynomial must be entirely ________ or entirely ________.

To solve a polynomial inequality, find the ________ numbers of the polynomial, and use these numbers to create ________ ________ for the inequality.

The key numbers of a rational expression are its ________ and its ________ ________.

The formula that relates cost, revenue, and profit is ________.

x

x x  5 x  0 2 x 12  0 x

(a

a) (b) (c)

3x2 x 2 x

9x3 25x 2 3

x 5 1 9

x x 2 2 x 1 1

x 2  16 2 < 9

x x 2  16

x 2 2  1 2  25

x 3 x 2 2  1 2

x

x x 2 6x 9 < 16 2

x 2 2x > 3 2 x < 6

x x 2 2x > 3 2

x2 2x 3 < 0

x2 > 2x 8

3x2 11x > 20

2x2 6x 15  0

x2 3x 18 > 0 2

x3 2x2 4x 8  0 x

x3 3x2 x > 3 x3

2x3 13x2 8x 46  6 x

4x2 4x 1  0

x2 3x 8 > 0

4x > 0 3 6x2 < 0

4x3 12x 2 4x > 0 3

x 4  0 3 4x  0

2x3 x x 4  0 3

x 1 x 3  0 2 x 23  0 2

x4 x 1 x 3  0 2

y  x y  0 y  3 2 2x 3

y  y  0 y  7 1 2x 2 2x 1 y

y  y  0 y  6 1 8x3 1 2x

y  x y  0 y  36

4x 1 x > 0

x2 1 x

x 5  0

5 7x 1 2x  4

x 6 x 1 2 < 0

x 12 x 2 3  0

2 x 5 > 1 x 3 x

5 x 6 > 3 x 2

x 3  9 4x 3

1 x  1 x 3

x2 2x x2 9  0

x2 x 6 x  0

x 1 2x x 1 > 1 x2

3x x 1  x x 4 3

y  y  0 y  6 3x x 2

y  y  0 y  8 2 x 2 x 1

y  y  1 y  2 2x2 x2 4

y  y  1 y  0 5x x2 4

4 x 2 4 2 x

x 4 x 2 4 2

2 x2 9x 20 x

81 4x 2 x2

2 9 x x2 2x 35 81

x x 2 9 x

0.4x2 5.26 < 10.2

1.3x2 3.78 > 2.12

0.5x2 12.5x 1.6 > 0

1.2x2 4.8x 3.1 < 5.3

2.3x 5.2 > 3.4

2 3.1x 3.7 > 5.8

A projectile is fired straight upward from ground level with an initial velocity of 160 feet per second. (a) At what instant will it be back at ground level? (b) When will the height exceed 384 feet?

A projectile is fired straight upward from ground level with an initial velocity of 128 feet per second. (a) At what instant will it be back at ground level? (b) When will the height be less than 128 feet?

GEOMETRY A rectangular playing field with a perimeter of 100 meters is to have an area of at least 500 square meters. Within what bounds must the length of the rectangle lie?

GEOMETRY A rectangular parking lot with a perimeter of 440 feet is to have an area of at least 8000 square feet. Within what bounds must the length of the rectangle lie?

COST, REVENUE, AND PROFIT The revenue and cost equations for a product are and where and are measured in dollars and represents the number of units sold. How many units must be sold to obtain a profit of at least $750,000? What is the price per unit?

COST, REVENUE, AND PROFIT The revenue and cost equations for a product are and where and are measured in dollars and represents the number of units sold. How many units must be sold to obtain a profit of at least $1,650,000? What is the price per unit?

SCHOOL ENROLLMENT The numbers (in millions) of students enrolled in schools in the United States from 1995 through 2006 are shown in the table.

SAFE LOAD The maximum safe load uniformly distributed over a one-foot section of a two-inch-wide wooden beam is approximated by the model where is the depth of the beam. (a) Evaluate the model for and Use the results to create a bar graph. (b) Determine the minimum depth of the beam that will safely support a load of 2000 pounds.

RESISTORS When two resistors of resistances and are connected in parallel (see figure), the total resistance satisfies the equation Find for a parallel circuit in which ohms and must be at least 1 ohm.

TEACHERS SALARIES The mean salaries (in thousands of dollars) of classroom teachers in the United States from 2000 through 2007 are shown in the table.

The zeros of the polynomial divide the real number line into four test intervals.

The solution set of the inequality is the entire set of real numbers.

x 2 bx 4  0 2 bx 4  0

x x 2 bx 4  0 2

3x 2 bx 5  0 2 bx 10  0

2x 3x 2 bx 5  0

GRAPHICAL ANALYSIS You can use a graphing utility to verify the results in Example 4. For instance, the graph of is shown below. Notice that the -values are greater than 0 for all values of as stated in Example 4(a). Use the graphing utility to graph and Explain how you can use the graphs to verify the results of parts (b), (c), and (d) of Example 4.

CAPSTONE Consider the polynomial and the real number line shown below. (a) Identify the points on the line at which the polynomial is zero. (b) In each of the three subintervals of the line, write the sign of each factor and the sign of the product. (c) At what -values does the polynomial change signs?