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Chapter 5: Q. 8 (page 494)

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 an irreducible quadratic factor x2+bx+cwith multiplicity m, then for some constants B1,B2,...,Bmand C1,C2,...,Cm, 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 an irreducible quadratic factor x2+bx+cwith multiplicity m, then for some constants B1,B2,...,Bm and C1,C2,...,Cm, the sum will include terms of the forms B1x+C1x2+bx+c+B2x+C2x2+bx+c2+...+Bmx+Cmx2+bx+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 an irreducible quadratic factor x2+bx+cwith multiplicity m, then for some constants B1,B2,...,Bm and C1,C2,...,Cm, 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 an irreducible quadratic factor x2+bx+cwith multiplicity m, then for some constants B1,B2,...,Bmand C1,C2,...,Cm, the sum will include terms of the forms B1x+C1x2+bx+c+B2x+C2x2+bx+c2+...+Bmx+Cmx2+bx+cm.

Proper rational functions are decomposed into partial fractions for irreducible quadratic factor with some multiplicity as shown above.

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