
Partial Fraction Decomposition
Flashcard
•
Mathematics
•
11th Grade
•
Hard
Standards-aligned
Wayground Content
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15 questions
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1.
FLASHCARD QUESTION
Front
What is partial fraction decomposition?
Back
Partial fraction decomposition is a technique used to express a rational function as the sum of simpler fractions, making it easier to integrate or analyze.
Tags
CCSS.HSA.APR.D.6
2.
FLASHCARD QUESTION
Front
What is the general form of partial fraction decomposition for a rational function with a repeated linear factor?
Back
The general form includes terms for each power of the factor, such as \( \frac{A}{(x-a)} + \frac{B}{(x-a)^2} + \ldots \) for a repeated factor \( (x-a)^n \).
Tags
CCSS.HSA.APR.D.6
3.
FLASHCARD QUESTION
Front
How do you determine the coefficients in partial fraction decomposition?
Back
You multiply both sides of the equation by the common denominator, then equate coefficients for corresponding powers of x to solve for the unknowns.
Tags
CCSS.HSA.APR.D.6
4.
FLASHCARD QUESTION
Front
What is the first step in performing partial fraction decomposition?
Back
The first step is to ensure that the degree of the numerator is less than the degree of the denominator. If not, perform polynomial long division first.
Tags
CCSS.HSA.APR.D.6
5.
FLASHCARD QUESTION
Front
What is the significance of the term \( \frac{A}{x} \) in partial fraction decomposition?
Back
It represents the contribution of the simple linear factor \( x \) in the denominator, where \( A \) is a constant to be determined.
Tags
CCSS.HSA.APR.D.6
6.
FLASHCARD QUESTION
Front
What is the significance of the term \( \frac{B}{x^2} \) in partial fraction decomposition?
Back
It accounts for the repeated linear factor \( x^2 \) in the denominator, where \( B \) is a constant to be determined.
Tags
CCSS.HSA.APR.D.6
7.
FLASHCARD QUESTION
Front
What is the significance of the term \( \frac{C}{(x-1)} \) in partial fraction decomposition?
Back
It represents the contribution of the linear factor \( (x-1) \) in the denominator, where \( C \) is a constant to be determined.
Tags
CCSS.HSA.APR.D.6
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