Question
Asked Jan 23, 2020
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When the degree of a polynomial ƒ(x) is less than the degree of a polynomial g(x), how do you write ƒ(x)/g(x) as a sum of partial fractions if g(x)

a. is a product of distinct linear factors?

b. consists of a repeated linear factor? a. contains an irreducible quadratic factor? What do you do if the degree of ƒ is not less than the degree of g?

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Expert Answer

Step 1

a) Given g(x) is product of distinct linear factors. 

Then we will write the linear factors as denominators of each fraction. And the numerators will be constants.

For example: 

 

Calculus homework question answer, step 1, image 1
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Step 2

b) Given that g(x) consists of a repeated linear factors. 

Let (ax-b)^k is a linear factor where k>1.

Then we have to consider denominators (ax-b) , (ax-b)^2 , (ax-b)^3 , .... , (ax-b)^k . And numerator of each will be constants. 

We have to repeat this for all other linear factors too. 

For example: 

Calculus homework question answer, step 2, image 1
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Step 3

a) Given that g(x)  contains an irreducible quadratic factor. Say (ax^2+bx+c) is an irreducible quadratic factor. 

T...

Calculus homework question answer, step 3, image 1
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