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Chapter 2: Problem 92

Perform the division by assuming that \(n\) is a positive integer. $$\frac{x^{3 n}-3 x^{2 n}+5 x^{n}-6}{x^{n}-2}$$

Short Answer

Expert verified
Performing the division results in: \(x^{2}-3x+5-3\).

Step by step solution

01

Determine the Highest Degree

Identify the highest degree in both the numerator and denominator, which in our case is \(x^{3n}\) in the numerator and \(x^{n}\) in the denominator.
02

Divide

Perform polynomial division by dividing each term in the numerator by \(x^{n}\) and reducing each power of x by n, which results in \(x^{2}-3x+5-6/x^{n}\).
03

Divide Constant Term by Substituting x

In the last term, \(x^{n}=2\), so substitute \(x^{n}\) by 2, which results in \(-6/2=-3\), hence the total answer is \(x^{2}-3x+5-3\).

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Most popular questions from this chapter

The revenue and cost equations for a product are \(R=x(75-0.0005 x)\) and \(C=30 x+250,000,\) where \(R\) and \(C\) are measured in dollars and \(x\) represents the number of units sold. How many units must be sold to obtain a profit of at least \(\$ 750,000 ?\) What is the price per unit?

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