Chapter 5: Q. 8 (page 441)

Verify that $(x^{2} - 1) + \frac{x^{2}}{x^{4} + 3 x^{2} + 4}$ is a valid result for the polynomial long-division calculation performed to divide the polynomial $x^{6} + 2 x^{4} + 2 x^{2} - 4$ by the polynomial $x^{4} + 3 x^{2} + 4$

Short Answer

Expert verified

The given result $(x^{2} - 1) + \frac{x^{2}}{x^{4} + 3 x^{2} + 4}$ is verified.

Step by step solution

Step 1. Given Information

The given improper function is $\frac{x^{6} + 2 x^{4} + 2 x^{2} - 4}{x^{4} + 3 x^{2} + 4}$

Step 2. Calculation

The long division methof is shown below,

So, the improper function is written as a sum of an integer and a proper function below,

$\frac{x^{6} + 2 x^{4} + 2 x^{2} - 4}{x^{4} + 3 x^{2} + 4} = (x^{2} - 1) + \frac{x^{2}}{x^{4} + 3 x^{2} + 4}$

Thus, the result is verified.

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Verify that $(x^{2} - 1) + \frac{x^{2}}{x^{4} + 3 x^{2} + 4}$ is a valid result for the polynomial long-division calculation performed to divide the polynomial $x^{6} + 2 x^{4} + 2 x^{2} - 4$ by the polynomial $x^{4} + 3 x^{2} + 4$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

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Verify that x2-1+x2x4+3x2+4is a valid result for the polynomial long-division calculation performed to divide the polynomial x6+2x4+2x2-4by the polynomialx4+3x2+4

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

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Decision Maths

Probability and Statistics

Calculus

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Study anywhere. Anytime. Across all devices.

Verify that $(x^{2} - 1) + \frac{x^{2}}{x^{4} + 3 x^{2} + 4}$ is a valid result for the polynomial long-division calculation performed to divide the polynomial $x^{6} + 2 x^{4} + 2 x^{2} - 4$ by the polynomial $x^{4} + 3 x^{2} + 4$