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CalculusQ&A LibraryWhen 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?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?

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:

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:

Step 3

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

T...

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