Explanation Approach: An algebraic expression is made up of one or more algebraic terms. Each term may consist of variables and constants. These terms are separated by operating symbols such as plus ( + ) and minus ( - ) . An algebraic expression with one or more terms is called a polynomial. In a polynomial, the exponent of the variable of each term must be a whole number. Polynomials in the variable x are usually denoted by p ( x ) , f ( x ) , g ( x ) etc. Thus p x = a n x n + a n - 1 x n - 1 + a n - 2 x n - 2 + . . a 1 x 1 + a 0 . If a n ≠ 0 then n is called the degree of the polynomial p(x) . The exponent with the greatest value in a polynomial is known as its degree. On the basis of the degree of the polynomial, we have standard names for the polynomials. A polynomial of degree 1 is called a linear polynomial. It is in the form of a x + b , where a and b are real numbers and a ≠ 0 . A polynomial of degree 2 is called a quadratic polynomial. It is in the form of a x 2 + b + c , where a, b and c are real numbers and a ≠ 0 . A polynomial of degree 3 is called a cubic polynomial. It is in the form of a x 3 + b x 2 + c x + d , where a .b , c and d are real numbers and a ≠ 0 . A polynomial of degree 4 is called a bi-quadratic polynomial. It is in the form of a x 4 + b x 2 + c x + d , where a .b c and d are real numbers and a ≠ 0 . The process to rewrite the rational function as a sum of two or more than two simpler rational fractions or expression is called partial fraction decomposition. The partial fraction can only be done for a proper rational function. Let the rational function, p ( x ) f ( x ) where f ( x ) ≠ 0 . If p x a n d q x are polynomials and the degree of p ( x ) < f ( x ) , it is called a proper rational function

12th Edition

ISBN: 9781305652231

Author: R. David Gustafson, Jeff Hughes

Publisher: Cengage Learning

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Chapter 6.6, Problem 54E

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The partial fraction decomposition when denominator of a rational expression has a repeated prime quadratic factor.

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Chapter 6.6, Problem 53E

Chapter 6.6, Problem 55E

Chapter 6 Solutions

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Ch. 6.1 - Self Check Use the graphing method to solve...Ch. 6.1 - Prob. 2SC Ch. 6.1 - Prob. 3SC Ch. 6.1 - Prob. 4SC Ch. 6.1 - Self Check 5 Use the elimination method to solve...Ch. 6.1 - Prob. 6SC Ch. 6.1 - Prob. 7SC Ch. 6.1 - Prob. 8SC Ch. 6.1 - Fill in the blanks. Any set of several equations...Ch. 6.1 - Prob. 2E

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The partial fraction decomposition when denominator of a rational expression has a repeated prime quadratic factor.

Solution Summary: The author explains the partial tion decomposition when denominator of rational expression has a repeated prime quadratic factor.

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To explain: The partial fraction decomposition when denominator of a rational expression has a repeated prime quadratic factor.

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Chapter 6 Solutions

To explain:

The partial fraction decomposition when denominator of a rational expression has a repeated prime quadratic factor.