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

12th Edition

ISBN: 9781305652231

Author: R. David Gustafson, Jeff Hughes

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.

Videos

Question

Chapter 6.6, Problem 52E

To determine

To explain:

The partial fraction decomposition when denominator of rational expression has repeated linear factors.

Expert Solution & Answer

Chapter 6 Solutions

College Algebra (MindTap Course List)

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

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The partial fraction decomposition when denominator of rational expression has repeated linear factors.

Solution Summary: The author explains the partial tion decomposition when denominator of rational expression has repeated linear factors. An algebraic expression with one or more terms is called a polynomial.

Concept explainers

Videos

To explain: The partial fraction decomposition when denominator of rational expression has repeated linear factors.

Chapter 6 Solutions

To explain:

The partial fraction decomposition when denominator of rational expression has repeated linear factors.