4. Polynomial Functions

The following exercises are geometric in nature and lead to polynomial models. Solve each problem. A standard piece of notebook paper measuring 8.5 in. by 11 in. is to be made into a box with an open top by cutting equal-size squares from each corner and folding up the sides. Let x represent the length of a side of each such square in inches. Use the table feature of a graphing calculator to do the following. Round to the nearest hundredth.

b. Determine when the volume of the box will be greater than 40 in.³.

The following exercises are geometric in nature and lead to polynomial models. Solve each problem. A standard piece of notebook paper measuring 8.5 in. by 11 in. is to be made into a box with an open top by cutting equal-size squares from each cor-ner and folding up the sides. Let x represent the length of a side of each such square in inches. Use the table feature of a graphing calculator to do the following. Round to the nearest hundredth.

a. Find the maximum volume of the box.

Exercises 107–109 will help you prepare for the material covered in the next section. Factor: x³+3x²−x−3

Exercises 107–109 will help you prepare for the material covered in the next section. Determine whether f(x)=x⁴−2x²+1 is even, odd, or neither. Describe the symmetry, if any, for the graph of f.

Rewrite 4-5x-x²+6x³ in descending powers of x.

Use (2x³−3x²−11x+6)/(x−3)=2x²+3x−2 to factor 2x³-3x²-11x+6 completely.

The following exercises are geometric in nature and lead to polynomial models. Solve each problem. A certain right triangle has area 84 in.². One leg of the triangle measures 1 in. less than the hypotenuse. Let x represent the length of the hypotenuse. Express the length of the leg mentioned above in terms of x. Give the domain of x.