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Fill in the blanks to complete each of the following theorem statements:

In a partial-fractions decomposition of a proper rational function p(x)q(x), if q(x)has a linear factor x-cwith multiplicity m, then for some constants A1,A2,...,Am, the sum will include terms of the forms _____.

Short Answer

Expert verified

In a partial-fractions decomposition of a proper rational function p(x)q(x), if q(x)has a linear factor x-cwith multiplicity m, then for some constants A1,A2,...,Am, the sum will include terms of the formsA1x-c+A2x-c2+...+Amx-cm.

Step by step solution

01

Step 1. Given information  

In a partial-fractions decomposition of a proper rational function p(x)q(x), if q(x)has a linear factor x-cwith multiplicity m, then for some constants A1,A2,...,Am, the sum will include terms of the forms _____.

02

Step 2. Filling in the blanks to complete the theorem statements  

In a partial-fractions decomposition of a proper rational function p(x)q(x), if q(x)has a linear factor x-cwith multiplicity m, then for some constants A1,A2,...,Am, the sum will include terms of the forms A1x-c+A2x-c2+...+Amx-cm.

Proper rational functions are decomposed into partial fractions for linear factors with some multiplicity as shown above.

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