Divers in Acapulco, Mexico, dive headfirst from the top of

Fill in each blank so that the resulting statement is true. We solve the polynomial inequality x2 8x 15 0 by first solving the equation ______________. The real solutions of this equation, 5 and 3, shown on the number line, are called ____________ points. 2 1 0 1 2 3 5 3 7 6 5 4 3

Fill in each blank so that the resulting statement is true. The points at 5 and 3 shown above divide the number line into three intervals: ____________, ____________, ____________.

Fill in each blank so that the resulting statement is true. True or false: A test value for the leftmost interval on the number line shown above could be 10. ____________

Fill in each blank so that the resulting statement is true. True or false: A test value for the rightmost interval on the number line shown above could be 0. ____________

Fill in each blank so that the resulting statement is true. Consider the rational inequality

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. (x 4)(x 2) 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. (x 3)(x 5) 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. (x 7)(x 3) 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. (x 1)(x 7) 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. x2 5x 4 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. x2 4x 3 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. x2 5x 4 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. x2 x 6 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. x2 6x 8 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. x2 2x 3 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. 3x2 10x 8 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. 9x2 3x 2 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. 2x2 x 15

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. 6x2 x 1

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. 4x2 7x 3

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. 3x2 16x 5

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. x2 4x 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. x2 2x 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. 2x2 3x 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. 3x2 5x 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. x2 x 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. x2 2x 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. x2 4x 2

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. x2 2x 2

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. 3x2 4x 2

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. 3x2 10x 5

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. 2x2 5x 1

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. 5x2 8x 11

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. x2 6x 9 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. 4x2 4x 1 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. (x 1)(x 2)(x 3) 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. (x 1)(x 2)(x 3) 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. x3 2x2 x 2 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. x3 2x2 4x 8 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. x3 3x2 9x 27 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. x3 7x2 x 7 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. x3 x2 4x 4 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. x3 x2 9x 9 0

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. x3 9x2

Solve each polynomial inequality in Exercises 140 and graph the solution set on a real number line. x3 4x2

Solve each rational inequality in Exercises 4156 and graph the solution set on a real number line. x 4 x 3 0

Solve each rational inequality in Exercises 4156 and graph the solution set on a real number line. x 5 x 2 0

Solve each rational inequality in Exercises 4156 and graph the solution set on a real number line. x 3 x 4 0

Solve each rational inequality in Exercises 4156 and graph the solution set on a real number line. x 5 x 2 0

Solve each rational inequality in Exercises 4156 and graph the solution set on a real number line. x 2 x 4 0

Solve each rational inequality in Exercises 4156 and graph the solution set on a real number line. x 3 x 2 0

Solve each rational inequality in Exercises 4156 and graph the solution set on a real number line. 4 2x 3x 4 0

Solve each rational inequality in Exercises 4156 and graph the solution set on a real number line. 3x 5 6 2x 0

Solve each rational inequality in Exercises 4156 and graph the solution set on a real number line. x x 3 0

Solve each rational inequality in Exercises 4156 and graph the solution set on a real number line. x 4 x 0

Solve each rational inequality in Exercises 4156 and graph the solution set on a real number line. x 1 x 3 2

Solve each rational inequality in Exercises 4156 and graph the solution set on a real number line. x x 1 2

Solve each rational inequality in Exercises 4156 and graph the solution set on a real number line. x 4 2x 1 3

Solve each rational inequality in Exercises 4156 and graph the solution set on a real number line. 1 x 3 1

Solve each rational inequality in Exercises 4156 and graph the solution set on a real number line. x 2 x 2 2

Solve each rational inequality in Exercises 4156 and graph the solution set on a real number line. x x 2 2

In Exercises 5760, use the given functions to find all values of x that satisfy the required inequality. f (x) 2x2, g(x) 5x 2; f (x) g(x)

In Exercises 5760, use the given functions to find all values of x that satisfy the required inequality. f (x) 4x2, g(x) 9x 2; f (x) g(x)

In Exercises 5760, use the given functions to find all values of x that satisfy the required inequality. f (x) 2x x 1 , g(x) 1; f (x) g(x)

In Exercises 5760, use the given functions to find all values of x that satisfy the required inequality. f (x) x 2x 1 , g(x) 1; f (x) g(x)

Solve each inequality in Exercises 6166 and graph the solution set on a real number line. x2 2x 36 12

Solve each inequality in Exercises 6166 and graph the solution set on a real number line. x2 6x 1 8

Solve each inequality in Exercises 6166 and graph the solution set on a real number line. 3 x 3 3 x 2

Solve each inequality in Exercises 6166 and graph the solution set on a real number line. 1 x 1 2 x 1

Solve each inequality in Exercises 6166 and graph the solution set on a real number line. x2 x 2 x2 4x 3 0

Solve each inequality in Exercises 6166 and graph the solution set on a real number line. x2 3x 2 x2 2x 3 0 f (x) = 2x3 + 11x2 7x 6 7 3 10 70

In Exercises 6768, use the graph of the polynomial function to solve each inequality. 2x3 11x2 7x 6

In Exercises 6768, use the graph of the polynomial function to solve each inequality. 2x3 11x2 7x 6 f (x) = x + 1 x2 4

1 4(x 2) 3 4(x 2)

1 4(x 2) 3 4(x 2)

You throw a ball straight up from a rooftop 160 feet high with an initial speed of 48 feet per second. The function s(t) 16t2 48t 160 models the balls height above the ground, s(t), in feet, t seconds after it was thrown. During which time period will the balls height exceed that of the rooftop?

Divers in Acapulco, Mexico, dive headfirst from the top of a cliff 87 feet above the Pacific Ocean. The function s(t) 16t2 8t 87 models a divers height above the ocean, s(t), in feet, t seconds after leaping. During which time period will the divers height exceed that of the cliff?

The functions model a cars stopping distance, f (x) or g(x), in feet, traveling at x miles per hour. Function f models stopping distance on dry pavement and function g models stopping distance on wet pavement. The graphs of these functions are shown for speeds of 30 miles per hour and greater. Notice that the figure does not specify which graph is the model for dry roads and which is the model for wet roads. Use this information to solve Exercises 7374.a. Use the given functions to find the stopping distance on dry pavement and the stopping distance on wet pavement for a car traveling at 35 miles per hour. Round to the nearest foot. b. Based on your answers to part (a), which rectangular coordinate graph shows stopping distances on dry pavement and which shows stopping distances on wet pavement? c. How well do your answers to part (a) model the actual stopping distances shown in Figure 11.17 on page 830? d. Determine speeds on dry pavement requiring stopping distances that exceed the length of one and one-half football fields, or 540 feet. Round to the nearest mile per hour. How is this shown on the appropriate graph of the models?

The functions model a cars stopping distance, f (x) or g(x), in feet, traveling at x miles per hour. Function f models stopping distance on dry pavement and function g models stopping distance on wet pavement. The graphs of these functions are shown for speeds of 30 miles per hour and greater. Notice that the figure does not specify which graph is the model for dry roads and which is the model for wet roads. Use this information to solve Exercises 7374.a. Use the given functions to find the stopping distance on dry pavement and the stopping distance on wet pavement for a car traveling at 55 miles per hour. Round to the nearest foot. b. Based on your answers to part (a), which rectangular coordinate graph shows stopping distances on dry pavement and which shows stopping distances on wet pavement? c. How well do your answers to part (a) model the actual stopping distances shown in Figure 11.17 on page 830? d. Determine speeds on wet pavement requiring stopping distances that exceed the length of one and one-half football fields, or 540 feet. Round to the nearest mile per hour. How is this shown on the appropriate graph of the models on page 650? A company manufactures wheelchairs. The average cost function, C, of producing x wheelchairs per month is given by C(x) 500,000 400x x

A company manufactures wheelchairs. The average cost function, C, of producing x wheelchairs per month is given by C(x) 500,000 400x x . The graph of the rational function is shown. Use the function to solve Exercises 7576. Describe the companys production level so that the average cost of producing each wheelchair does not exceed $425. Use a rational inequality to solve the problem. Then explain how your solution is shown on the graph.

A company manufactures wheelchairs. The average cost function, C, of producing x wheelchairs per month is given by C(x) 500,000 400x x . The graph of the rational function is shown. Use the function to solve Exercises 7576. Describe the companys production level so that the average cost of producing each wheelchair does not exceed $410. Use a rational inequality to solve the problem. Then explain how your solution is shown on the graph.

The perimeter of a rectangle is 50 feet. Describe the possible length of a side if the area of the rectangle is not to exceed 114 square feet.

The perimeter of a rectangle is 180 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 800 square feet. Writing in Mathematics

What is a polynomial inequality?

What is a rational inequality?

Describe similarities and differences between the solutions of (x 2)(x 5) 0 and x 2 x 5 0.

Solve each inequality in Exercises 8287 using a graphing utility. x2 3x 10 0

Solve each inequality in Exercises 8287 using a graphing utility. 2x2 5x 3 0

Solve each inequality in Exercises 8287 using a graphing utility. x 4 x 1 0

Solve each inequality in Exercises 8287 using a graphing utility. x 2 x 3 2

Solve each inequality in Exercises 8287 using a graphing utility. 1 x 1 2 x 4

Solve each inequality in Exercises 8287 using a graphing utility. x3 2x2 5x 6 0

The graph shows stopping distances for trucks at various speeds on dry roads and on wet roads. Use this information to solve Exercises 8889. a. Use the statistical menu of your graphing utility and the quadratic regression program to obtain the quadratic function that models a trucks stopping distance, f (x), in feet, on dry pavement traveling at x miles per hour. Round the x-coefficient and the constant term to one decimal place. b. Use the function from part (a) to determine speeds on dry pavement requiring stopping distances that exceed 455 feet. Round to the nearest mile per hour.

The graph shows stopping distances for trucks at various speeds on dry roads and on wet roads. Use this information to solve Exercises 8889. a. Use the statistical menu of your graphing utility and the quadratic regression program to obtain the quadratic function that models a trucks stopping distance, f (x), in feet, on wet pavement traveling at x miles per hour. Round the constant term to one decimal place. b. Use the function from part (a) to determine speeds on wet pavement requiring stopping distances that exceed 446 feet.

When solving f (x) 0, where f is a polynomial function, I only pay attention to the sign of f at each test value and not the actual function value.

Im solving a polynomial inequality that has a value for which the polynomial function is undefined.

Because it takes me longer to come to a stop on a wet road than on a dry road, graph (a) for Exercises 7374 is the model for stopping distances on wet pavement and graph (b) is the model for stopping distances on dry pavement.

I began the solution of the rational inequality x 1 x 3 2 by setting both x 1 and x 3 equal to zero.

In Exercises 9497, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The solution set of x2 25 is (5, ).

In Exercises 9497, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The inequality x 2 x 3 2 can be solved by multiplying both sides by x 3, resulting in the equivalent inequality x 2 2(x 3).

In Exercises 9497, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. (x 3)(x 1) 0 and x 3 x 1 0 have the same solution set.

In Exercises 9497, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The inequality x 2 x 3 2 can be solved by multiplying both sides by (x 3)2, x 3, resulting in the equivalent inequality (x 2)(x 3) 2(x 3)2.

Write a quadratic inequality whose solution set is [3, 5].

Write a rational inequality whose solution set is ( , 4) [3, ).

In Exercises 100103, use inspection to describe each inequalitys solution set. Do not solve any of the inequalities. (x 2)2 0

In Exercises 100103, use inspection to describe each inequalitys solution set. Do not solve any of the inequalities. (x 2)2 0

In Exercises 100103, use inspection to describe each inequalitys solution set. Do not solve any of the inequalities. (x 2)2 1

In Exercises 100103, use inspection to describe each inequalitys solution set. Do not solve any of the inequalities. 1 (x 2)2 0

The graphing calculator screen shows the graph of y 4x2 8x 7. y = 4x2 8x + 7 [2, 6, 1] by [2, 8, 1] a. Use the graph to describe the solution set for 4x2 8x 7 0. b. Use the graph to describe the solution set for 4x2 8x 7 0. c. Use an algebraic approach to verify each of your descriptions in parts (a) and (b).

The graphing calculator screen shows the graph of y 27 3x2 . Write and solve a quadratic inequality that explains why the graph only appears for 3 x 3. y = 27 3x2 [5, 5, 1] by [0, 6, 1]

Solve: x 5 3 8. (Section 9.3, Example 4)

Divide: 2x 6 x2 8x 16 x2 9 x2 3x 4 . (Section 7.2, Example 6)

Factor completely: x4 16y4. (Section 6.5, Example 7)

Exercises 109111 will help you prepare for the material covered in the first section of the next chapter. In each exercise, use point plotting to graph the function. Begin by setting up a table of coordinates, selecting integers from 3 to 3, inclusive, for x. f (x) 2x

Exercises 109111 will help you prepare for the material covered in the first section of the next chapter. In each exercise, use point plotting to graph the function. Begin by setting up a table of coordinates, selecting integers from 3 to 3, inclusive, for x. f (x) 2x

Exercises 109111 will help you prepare for the material covered in the first section of the next chapter. In each exercise, use point plotting to graph the function. Begin by setting up a table of coordinates, selecting integers from 3 to 3, inclusive, for x. f (x) 2x 1