CAPSTONE Consider the polynomial and the real number line shown below. (a) Identify the

Fill in the blanks. Between two consecutive zeros, a polynomial must be entirely ________ or entirely ________.

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

Fill in the blanks. The key numbers of a rational expression are its ________ and its ________ ________.

Fill in the blanks. The formula that relates cost, revenue, and profit is ________.

In Exercises 58, determine whether each value of is a solution of the inequality.

In Exercises 58, determine whether each value of is a solution of the inequality.

In Exercises 58, determine whether each value of is a solution of the inequality.

In Exercises 58, determine whether each value of is a solution of the inequality.

In Exercises 912, find the key numbers of the expression.

In Exercises 912, find the key numbers of the expression.

In Exercises 912, find the key numbers of the expression.

In Exercises 912, find the key numbers of the expression.

In Exercises 1330, solve the inequality and graph the solution on the real number line.

In Exercises 1330, solve the inequality and graph the solution on the real number line.

In Exercises 1330, solve the inequality and graph the solution on the real number line.

In Exercises 1330, solve the inequality and graph the solution on the real number line.

In Exercises 1330, solve the inequality and graph the solution on the real number line.

In Exercises 1330, solve the inequality and graph the solution on the real number line.

In Exercises 1330, solve the inequality and graph the solution on the real number line.

In Exercises 1330, solve the inequality and graph the solution on the real number line.

In Exercises 1330, solve the inequality and graph the solution on the real number line.

In Exercises 1330, solve the inequality and graph the solution on the real number line.

In Exercises 1330, solve the inequality and graph the solution on the real number line.

In Exercises 1330, solve the inequality and graph the solution on the real number line.

In Exercises 1330, solve the inequality and graph the solution on the real number line.

In Exercises 1330, solve the inequality and graph the solution on the real number line.

In Exercises 1330, solve the inequality and graph the solution on the real number line.

In Exercises 1330, solve the inequality and graph the solution on the real number line.

In Exercises 1330, solve the inequality and graph the solution on the real number line.

In Exercises 1330, solve the inequality and graph the solution on the real number line.

In Exercises 3136, solve the inequality and write the solution set in interval notation.

In Exercises 3136, solve the inequality and write the solution set in interval notation.

In Exercises 3136, solve the inequality and write the solution set in interval notation.

In Exercises 3136, solve the inequality and write the solution set in interval notation.

In Exercises 3136, solve the inequality and write the solution set in interval notation.

In Exercises 3136, solve the inequality and write the solution set in interval notation.

GRAPHICAL ANALYSIS In Exercises 3740, use a graphing utility to graph the equation. Use the graph to approximate the values of that satisfy each inequality.

GRAPHICAL ANALYSIS In Exercises 3740, use a graphing utility to graph the equation. Use the graph to approximate the values of that satisfy each inequality.

GRAPHICAL ANALYSIS In Exercises 3740, use a graphing utility to graph the equation. Use the graph to approximate the values of that satisfy each inequality.

GRAPHICAL ANALYSIS In Exercises 3740, use a graphing utility to graph the equation. Use the graph to approximate the values of that satisfy each inequality.

In Exercises 4154, solve the inequality and graph the solution on the real number line.

In Exercises 4154, solve the inequality and graph the solution on the real number line.

In Exercises 4154, solve the inequality and graph the solution on the real number line.

In Exercises 4154, solve the inequality and graph the solution on the real number line.

In Exercises 4154, solve the inequality and graph the solution on the real number line.

In Exercises 4154, solve the inequality and graph the solution on the real number line.

In Exercises 4154, solve the inequality and graph the solution on the real number line.

In Exercises 4154, solve the inequality and graph the solution on the real number line.

In Exercises 4154, solve the inequality and graph the solution on the real number line.

In Exercises 4154, solve the inequality and graph the solution on the real number line.

In Exercises 4154, solve the inequality and graph the solution on the real number line.

In Exercises 4154, solve the inequality and graph the solution on the real number line.

In Exercises 4154, solve the inequality and graph the solution on the real number line.

In Exercises 4154, solve the inequality and graph the solution on the real number line.

GRAPHICAL ANALYSIS In Exercises 5558, use a graphing utility to graph the equation. Use the graph to approximate the values of that satisfy each inequality.

GRAPHICAL ANALYSIS In Exercises 5558, use a graphing utility to graph the equation. Use the graph to approximate the values of that satisfy each inequality.

GRAPHICAL ANALYSIS In Exercises 5558, use a graphing utility to graph the equation. Use the graph to approximate the values of that satisfy each inequality.

GRAPHICAL ANALYSIS In Exercises 5558, use a graphing utility to graph the equation. Use the graph to approximate the values of that satisfy each inequality.

In Exercises 5964, find the domain of in the expression. Use a graphing utility to verify your result.

In Exercises 5964, find the domain of in the expression. Use a graphing utility to verify your result.

In Exercises 5964, find the domain of in the expression. Use a graphing utility to verify your result.

In Exercises 5964, find the domain of in the expression. Use a graphing utility to verify your result.

In Exercises 5964, find the domain of in the expression. Use a graphing utility to verify your result.

In Exercises 5964, find the domain of in the expression. Use a graphing utility to verify your result.

In Exercises 6570, solve the inequality. (Round your answers to two decimal places.)

In Exercises 6570, solve the inequality. (Round your answers to two decimal places.)

In Exercises 6570, solve the inequality. (Round your answers to two decimal places.)

In Exercises 6570, solve the inequality. (Round your answers to two decimal places.)

In Exercises 6570, solve the inequality. (Round your answers to two decimal places.)

In Exercises 6570, solve the inequality. (Round your answers to two decimal places.)

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. (Source: U.S. Census Bureau) (a) Use a graphing utility to create a scatter plot of the data. Let represent the year, with corresponding to 1995. (b) Use the regression feature of a graphing utility to find a quartic model for the data. (c) Graph the model and the scatter plot in the same viewing window. How well does the model fit the data? (d) According to the model, during what range of years will the number of students enrolled in schools exceed 74 million? (e) Is the model valid for long-term predictions of student enrollment in schools? Explain.

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. A model that approximates these data is given by where represents the year, with corresponding to 2000. (Source: Educational Research Service, Arlington, VA) (a) Use a graphing utility to create a scatter plot of the data. Then graph the model in the same viewing window. (b) How well does the model fit the data? Explain. (c) According to the model, in what year will the salary for classroom teachers exceed $60,000? (d) Is the model valid for long-term predictions of classroom teacher salaries? Explain.

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.

In Exercises 8386, (a) find the interval(s) for such that the equation has at least one real solution and (b) write a conjecture about the interval(s) based on the values of the coefficients.

In Exercises 8386, (a) find the interval(s) for such that the equation has at least one real solution and (b) write a conjecture about the interval(s) based on the values of the coefficients.

In Exercises 8386, (a) find the interval(s) for such that the equation has at least one real solution and (b) write a conjecture about the interval(s) based on the values of the coefficients.

In Exercises 8386, (a) find the interval(s) for such that the equation has at least one real solution and (b) write a conjecture about the interval(s) based on the values of the coefficients.

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?