Partial Fractions | Quadratic and Repeated Linear Factors

So far we have performed partial fraction decomposition with expressions that have had linear factors in the denominator, and we applied numerators A, B, or C representing constants. Now we will look at an example where one of the factors in the denominator is a quadratic expression that does not factor. This is referred to as an irreducible quadratic factor. In cases like this, we use a linear numerator such as Ax+B, Bx+C etc.

Then partial Fraction Decomposition Form for Repeated Factors:
A factor is repeated if it has multiplicity greater than 1.

If the repeated factor is linear, then each of these rational expressions will have a constant numerator coefficient.

If the factor is to the power of 3. Therefore, 3 rational expressions are needed in the partial fraction decomposition, with each of the denominator is raised to a different positive integer power up to 3, wih 1, 2 and 3 respectively. Since it's linear factor, each of these rational expressions will have a constant numerator coefficient.

[IgnatiusIgme]

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[georgesadler]

Professor Tambuwal thank you for explaining and solving Partial Fractions Decomposition problems which involves Quadratic and Repeated Linear Factors.

[mountainwolvesbd]

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[mikemwilamike]

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[LegoFilou]

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[Retroviridae]

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[MichDiva]

This is nice
But i dont understand how u expanded ur first expansion which is (Ax+B)(x²+4+4)

[SingathiweNgcobo]

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[ridonngandu]

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[mastrex]

I think the x² is meant to be a/x + b/x² not Ax+b/x²

[tijjanisabo]

My questions is. Giving that they’re two children in a family, what is the conditional probability that both are boys giving that at least one is a boys. Pls I’m confused.

[gorettirita]

Thanks for class but I have a question is it possible to be given a linear factor and repeated linear factor as in the denominator been [x-2] [x-4] to the power of 2 [just the second factor to the power of 2]

[divine-favouremmanuel]

How about something like
(3x² - 7)/׳+2ײ-8×

[djalalmaster]

Why we didn't break down the x², isn't repeated?

[annietembo-osze]

Please help me with this one X²+5/X²-5X-3