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Chapter 5: Q. 6 (page 441)

Describe two ways in which the long-division algorithm for polynomials is similar to the long-division algorithm for integers and then two ways in which the two algorithms are different.

Short Answer

Expert verified

The long division algorithm to divide polynomial is analogous to the long division algorithm for integers.

Step by step solution

01

Step 1. Given Information

The given term is long-division algorithm for polynomials

02

Step 2. Explanation

Any two numbers can be divided as long as the divisor is not equal to 0.

similarly any two polynomial can be divided as long as the divisor is not equal to 0.

The long division algorithm to divide polynomial is analogous to the long division algorithm for integers.

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Most popular questions from this chapter

Solve each of the integrals in Exercises 39–74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.

$\int \frac{x^{2} + 9}{x^{\frac{3}{2}}} d x$

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Consider the integral $\int \sin x \cos x d x$ .

(a) Solve this integral by using u-substitution with $u = \sin x$ and $d u = \cos x d x$ .

(b) Solve the integral another way, using u-substitution with $u = \cos x$ and $d u = - \sin x d x$ .

(c) How must your two answers be related? Use algebra to prove this relationship.

Solve the integral: $\int \frac{x^{2}}{e^{x}} d x$

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