Explanation Given: 7 x 3 + 4 x 2 + 63 x + 15 x 4 + 11 x 2 + 18 Concept Used: To convert a complicated single fraction in partial fraction decomposition we follow the steps Factor the denominator completely into linear factors of the form ( a x + b ) m and quadratic factors of the form ( a x 2 + b x + c ) n that are not further factorable over the integers Set up the decomposition. That is, write the original rational expression as a sum of simpler fraction, as A 1 ( a x + b ) 1 + A 2 ( a x + b ) 2 + ......... + A m ( a x + b ) m , where A 1 , A 2 .... A m are constants And then solve to find the value of these constants For a first-degree (linear) denominator, the numerator is constant (degree 0) For a second-degree (linear) denominator, the numerator is linear (degree 1) Calculation: To set up partial fraction form for 7 x 3 + 4 x 2 + 63 x + 15 x 4 + 11 x 2 + 18 First we have to factor the denominator completely into linear factors, as x 4 + 11 x 2 + 18 = x 4 + 2 x 2 + 9 x 2 + 18 = x 2 ( x 2 + 2 ) + 9 ( x 2 + 2 ) = ( x 2 + 2 ) ( x 2 + 9 ) Now, we can set the partial decomposition for given fraction as 7 x 3 + 4 x 2 + 63 x + 15 x 4 + 11 x 2 + 18 = 7 x 3 + 4 x 2 + 63 x + 15 ( x 2 + 2 ) ( x 2 + 9 ) = A x + B ( x 2 + 2 ) + C x + D ( x 2 + 9 ) Since, for a first-degree (linear) denominator, the numerator is constant (degree 0) and for a second-degree (linear) denominator, the numerator is linear (degree 1) Now we have to solve value of A, B, C and D in A x + B ( x 2 + 2 ) + C x + D ( x 2 + 9 ) , as 7 x 3 + 4 x 2 + 63 x + 15 ( x 2 + 2 ) ( x 2 + 9 ) = A x + B ( x 2 + 2 ) + C x + D ( x 2 + 9 ) = ( A x + B ) ( x 2 + 9 ) + (

College Algebra & Trigonometry - Standalone book

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ISBN: 9780078035623

Author: Julie Miller, Donna Gerken

Publisher: McGraw-Hill Education

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Chapter 9, Problem 28T

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Find the partial fraction decomposition for

7x3+4x2+63x+15x4+11x2+18

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Chapter 9, Problem 27T

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College Algebra & Trigonometry - Standalone book

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Find the partial fraction decomposition for 7 x 3 + 4 x 2 + 63 x + 15 x 4 + 11 x 2 + 18

Solution Summary: The author explains how to convert a complicated single tion in partial tion decomposition by factoring the denominator into linear and quadratic factors.

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Find the partial fraction decomposition for

7x3+4x2+63x+15x4+11x2+18

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Find the partial fraction decomposition for 7 x 3 + 4 x 2 + 63 x + 15 x 4 + 11 x 2 + 18

Solution Summary: The author explains how to convert a complicated single tion in partial tion decomposition by factoring the denominator into linear and quadratic factors.

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Find the partial fraction decomposition for 7x3+4x2+63x+15x4+11x2+18

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Chapter 9 Solutions

Find the partial fraction decomposition for

7x3+4x2+63x+15x4+11x2+18