Chapter 1

The length of a rectangle is 6 feet less than three times the width. The area of the rectangle is 144 square feet. Find the dimensions of the rectangle.

Perform the indicated operations and write the result in simplest form. \(b^{2}+b(3 b+5)\)

Mrs. Menendez uses computer software to record her checking account balance. Each time that she makes an entry, the amount that she enters is added to her balance. If she writes a check for \(\$ 20,\) how should she enter this amount?

In \(9-26,\) write each expression as the product of two binomials. $$ 3 x^{2}-5 x-12 $$

In \(13-22,\) solve each equation or inequality. Each solution is an integer. $$ (b-1)-(3 b-4)=b $$

In \(18-23,\) write and solve an equation or an inequality to solve the problem. At a parking garage, parking costs \(\$ 5\) for the first hour and \(\$ 3\) for each additional hour or part of an hour. Mr. Kanesha paid \(\$ 44\) for parking on Monday. For how many hours did Mr. Kanesha park his car?

In \(15-26,\) solve each inequality and write the solution set if the variable is an element of the set of integers. $$ |6-3 x|<15 $$

The length of the shorter leg, a, of a right triangle is 6 centimeters less than the length of the hypotenuse, c, and the length of the longer leg, b, is 3 centimeters less than the length of the hypotenuse. Find the length of the sides of the right triangle.

Perform the indicated operations and write the result in simplest form. \(4 y(2 y-3)-5(2-y)\)

Mrs. Menendez uses computer software to record her checking account balance. Each time that she makes an entry, the amount that she enters is added to her balance. Mrs. Menendez had a balance of \(\$ 52\) in her checking account and wrote a check for \(\$ 75 .\) a. How should she enter the \(\$ 75 ?\) b. How should her new balance be recorded?

In \(9-26,\) write each expression as the product of two binomials. $$ 2 y^{2}+5 y-3 $$

In \(13-22,\) solve each equation or inequality. Each solution is an integer. $$ -3-2 x \geq 12+x $$

In \(18-23,\) write and solve an equation or an inequality to solve the problem. Kim wants to buy an azalea plant for \(\$ 19\) and some delphinium plants for \(\$ 5\) each. She wants to spend less than \(\$ 49\) for the plants. At most how many delphinium plants can she buy?

In \(15-26,\) solve each inequality and write the solution set if the variable is an element of the set of integers. $$ |8+4 b| \geq 0 $$

The height \(h,\) in feet, of a golf ball shot upward from a ground level sprint gun is described by the formula \(h=-16 t^{2}+48 t\) where \(t\) is the time in seconds. When will the ball hit the ground again?

Perform the indicated operations and write the result in simplest form. \(a^{3}\left(a^{2}+3\right)-\left(a^{5}+3 a^{3}\right)\)

Mrs. Menendez uses computer software to record her checking account balance. Each time that she makes an entry, the amount that she enters is added to her balance. After writing the \(\$ 75\) check, Mrs. Menendez realized that she would be overdrawn when the check was paid by the bank so she transferred \(\$ 100\) from her savings account to her checking account. How should the \(\$ 100\) be entered in her computer program?

In \(9-26,\) write each expression as the product of two binomials. $$ 5 b^{2}+6 b+1 $$

An online music store is having a sale. Any song costs 75 cents and any ringtone costs 50 cents. Emma can buy 6 songs and 2 audiobooks for the same price as 5 ringtones and 3 audiobooks. What is the cost of an audiobook?

In \(18-23,\) write and solve an equation or an inequality to solve the problem. To prepare for a tennis match and have enough time for schoolwork, Priscilla can practice no more than 14 hours. If she practices the same length of time on Monday through Friday, and then spends 4 hours on Saturday, what is the most time she can practice on Wednesday?

In \(15-26,\) solve each inequality and write the solution set if the variable is an element of the set of integers. $$ |5-b|+4<9 $$

Perform the indicated operations and write the result in simplest form. \((z-2)^{3}\)

In \(9-26,\) write each expression as the product of two binomials. $$ 6 x^{2}-13 x+2 $$

The length of a rectangle is 5 feet more than twice the width. a. If \(x\) represents the width of the rectangle, represent the perimeter of the rectangle in terms of \(x .\) b. If the perimeter of the rectangle is 2 feet more than eight times the width of the rec- tangle, find the dimensions of the rectangle.

In \(15-26,\) solve each inequality and write the solution set if the variable is an element of the set of integers. $$ |11-2 b|-6>11 $$

Solve for the variable and check. Each solution is an integer. \((2 x+1)+(4-3 x)=10\)

In \(9-26,\) write each expression as the product of two binomials. $$ 4 y^{2}+4 y+1 $$

On his trip to work each day, Brady pays the same toll, using etther all quarters or all dimes. If the number of dimes needed for the toll is 3 more than the number of quarters, what is the toll?

In \(15-26,\) solve each inequality and write the solution set if the variable is an element of the set of integers. $$ |6-3 b|+4<3 $$

Solve for the variable and check. Each solution is an integer. \((3 a+7)-(a-1)=14\)

In \(9-26,\) write each expression as the product of two binomials. $$ 9 x^{2}-12 x+4 $$

In \(15-26,\) solve each inequality and write the solution set if the variable is an element of the set of integers. $$ |7-x|+2 \leq 12 $$

Solve for the variable and check. Each solution is an integer. \(2(b-3)+3(b+4)=b+14\)

In \(27-39,\) factor each polynomial completely. $$ a^{3}+3 a^{2}-a-3 $$

A carpenter is making a part for a desk. The part is to be 256 millimeters wide plus or minus 3 millimeters. This means that the absolute value of the difference between the dimension of the part and 256 can be no more than 3 millimeters. To the nearest millimeter, what are the acceptable dimensions of the part?

Solve for the variable and check. Each solution is an integer. \((x+3)^{2}=(x-5)^{2}\)

In \(27-39,\) factor each polynomial completely. $$ 5 x^{2}-15 x+10 $$

A theater owner knows that to make a profit as well as to comply with fire regulations, the number of tickets that he sells can differ from 225 by no more than \(75 .\) How many tickets can the theater owner sell in order to make a profit and comply with fire regulations?

Solve for the variable and check. Each solution is an integer. \(4 x(x+2)-x(3+4 x)=2 x+18\)

In \(27-39,\) factor each polynomial completely. $$ b^{3}-4 b $$

A cereal bar is listed as containing 200 calories. A laboratory tested a sample of the bars and found that the actual calorie content varied by as much as 28 calories. Write and solve an absolute value inequality for the calorie content of the bars.

Solve for the variable and check. Each solution is an integer. \(y(y+2)-y(y-2)=20-y\)

In \(27-39,\) factor each polynomial completely. $$ 4 a x^{2}+4 a x-24 a $$

The length of a rectangle is 4 more than twice the width, \(x .\) Express the area of the rectangle in terms of \(x .\)

In \(27-39,\) factor each polynomial completely. $$ 12 c^{2}-3 $$

The length of the longer leg, \(a,\) of a right triangle is 1 centimeter less than the length of the hypotenuse and the length of the shorter leg, \(b,\) is 8 centimeters less than the length of the hypotenuse. a. Express \(a\) and \(b\) in terms of \(c,\) the length of the hypotenuse. b. Express \(a^{2}+b^{2}\) as a polynomial in terms of \(c\) . c. Use the Pythagorean Theorem to write a polynomial equal to \(c^{2}\) .

In \(27-39,\) factor each polynomial completely. $$ x^{4}-81 $$

In \(27-39,\) factor each polynomial completely. $$ x^{4}-16 $$

In \(27-39,\) factor each polynomial completely. $$ 2 x^{3}+13 x^{2}+15 x $$

In \(27-39,\) factor each polynomial completely. $$ 4 x^{3}-10 x^{2}+6 x $$