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- Use a graphing calculator to find the coordinates of the turning points of the graph of each polynomial function in the given domain interval. Give answers to the nearest hundredth. ƒ(x)=x^3+4x^2-8x-8; [-3.8, -3]
Problem 87
- Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=x^5+3x^4-x^3+2x+3
Problem 87
- Use a graphing calculator to find the coordinates of the turning points of the graph of each polynomial function in the given domain interval. Give answers to the nearest hundredth. ƒ(x)=x^4-7x^3+13x^2+6x-28; [-1, 0]
Problem 88
- Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=2x^5-x^4+x^3-x^2+x+5
Problem 88
- Perform each division. See Examples 9 and 10. (q^2+4q-32)/(q-4)
Problem 89
- Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=2x^5-7x^3+6x+8
Problem 89
Problem 90
Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=11x5-x3+7x-5
- Perform each division. See Examples 9 and 10. (3t^2+17t+10)/(3t+2)
Problem 91
Problem 91
Use the technique described in Exercises 87–90 to solve each inequality. Write the solution set in interval notation. x2 - x - 6 < 0
- Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=5x^6-6x^5+7x^3-4x^2+x+2
Problem 91
Problem 92
Use the technique described in Exercises 87–90 to solve each inequality. Write the solution set in interval notation. x2 - 9x + 20 < 0
Problem 92
Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=9x6-7x4+8x2+x+6
- Perform each division. See Examples 9 and 10. (p^2+2p+20)/(p+6)
Problem 93
Problem 93
Use the technique described in Exercises 87–90 to solve each inequality. Write the solution set in interval notation. 2x2 - 9x ≥ 18
- Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=7x^5+6x^4+2x^3+9x^2+x+5
Problem 93
Problem 93a
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.
- Perform each division. See Examples 9 and 10. (x^2+11x+16)/(x+8)
Problem 94
Problem 94
Use the technique described in Exercises 87–90 to solve each inequality. Write the solution set in interval notation. 3x2 + x ≥ 4
- Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=-2x^5+10x^4-6x^3+8x^2-x+1
Problem 94
Problem 95
Use the technique described in Exercises 87–90 to solve each inequality. Write the solution set in interval notation. -x2 + 4x + 1 ≥ 0
Problem 95
Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.* ƒ(x)=x4+2x3-3x2+24x-180
Problem 96
Use the technique described in Exercises 87–90 to solve each inequality. Write the solution set in interval notation. -x2 + 2x + 6 > 0
Problem 96a
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.
Problem 96b
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.
- Perform each division. See Examples 9 and 10. (4x^3+9x^2-10x-6)/(4x+1)
Problem 97
- Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.* ƒ(x)=x^4+x^3-9x^2+11x-4
Problem 97
- Perform each division. See Examples 9 and 10. (4x^3-3x^2+1)/(x-2)
Problem 99
- Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.* ƒ(x)=2x^5+11x^4+16x^3+15x^2+36x
Problem 99
Problem 100
Perform each division. See Examples 9 and 10.
Problem 101
Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.* ƒ(x)=x5-6x4+14x3-20x2+24x-16
