Chapter 7: Q53. (page 352)

The maximum number of regions formed by connecting (n) points of a circle can be obtained by the function $f (n) = \frac{1}{24} (n^{4} - 6 n^{3} + 23 n^{2} - 18 n + 24)$ . What is the degree of this polynomial.

Short Answer

Expert verified

The degree of the polynomial is 4.

Step by step solution

Step 1. Write down the given information.

The given polynomial is $f (n) = \frac{1}{24} (n^{4} - 6 n^{3} + 23 n^{2} - 18 n + 24)$ .

Step 2. Calculation.

The given polynomial $f (n) = \frac{1}{24} (n^{4} - 6 n^{3} + 23 n^{2} - 18 n + 24)$ can be re-written as:

$\begin{matrix} f (n) = \frac{1}{24} (n^{4} - 6 n^{3} + 23 n^{2} - 18 n + 24) \\ f (n) = \frac{n^{4}}{24} - \frac{6 n^{3}}{24} + \frac{23 n^{2}}{24} - \frac{18 n}{24} + \frac{24}{24} \\ f (n) = \frac{1}{24} n^{4} - \frac{1}{4} n^{3} + \frac{23}{24} n^{2} - \frac{3}{4} n + 1.... (1) \end{matrix}$

From (1) it can be interpreted that the degree of polynomial is 4 whose leading coefficient is $\frac{1}{24}$ .

Step 3. Conclusion.

The degree of the polynomial is $4$ .

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The maximum number of regions formed by connecting (n) points of a circle can be obtained by the function $f (n) = \frac{1}{24} (n^{4} - 6 n^{3} + 23 n^{2} - 18 n + 24)$ . What is the degree of this polynomial.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

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The maximum number of regions formed by connecting (n) points of a circle can be obtained by the function fn=124n4-6n3+23n2-18n+24. What is the degree of this polynomial.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

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Probability and Statistics

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Mechanics Maths

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Study anywhere. Anytime. Across all devices.

The maximum number of regions formed by connecting (n) points of a circle can be obtained by the function $f (n) = \frac{1}{24} (n^{4} - 6 n^{3} + 23 n^{2} - 18 n + 24)$ . What is the degree of this polynomial.