Partial Fractions - Denominator with quadratic factors | SHS 1 ELECTIVE MATH

SERIES ON PARTIAL FRACTIONS
TOPIC: PARTIAL FRACTIONS - DENOMINATOR WITH QUADRATIC FACTORS
In this video, we are going to learn how to decompose a rational function with a quadratic factor to smaller of component fractions.
If the denominator of a rational function has only linear roots, the numerator of each linear factor is a constant if the rational function is to be resolved into partial fractions.
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After watching 5 unhelpful videos , this one really helped me. ThANK YOU MAN.

[@SkanCityAcademy_SirJohn]

You are most welcome

[@efeoghene1622]

Hello. I have a similar problem regarding this partial fraction with a quadratic denominator. Can i send you the question so you could help out ?

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[@SkanCityAcademy_SirJohn]

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How to calculate B and C if we don't have quadratic equations on the RHS

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[@SkanCityAcademy_SirJohn]

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[@SkanCityAcademy_SirJohn]

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[@Tastygarden1]

I have a question. Why we put the denominator linear factor equal to zero. Even when we let the denominator equal to 0 the whole expression will become undefined. And why not we put the quadratic factor equal to zero. Please reply me as soon as possible. Thanks.

[@SkanCityAcademy_SirJohn]

Hello, the idea is always to eliminate two constants and have only one constant remaining at a time.
Can you come again with your question. I don't really get you.

[@Tastygarden1]

the question is that when we let the denominator factor =0. What is the logic how could we let it =0. please answer me. it is very urgent.@@SkanCityAcademy_SirJohn

[@SkanCityAcademy_SirJohn]

Is it a general question, or a question from my video, if it's a question from my video, please state the time in the video.

[@abdullah4759]

What if numerator is only a single number with no x^2? Then how do you compare

[@SkanCityAcademy_SirJohn]

You will still use the same approach, just that this time the LHS will be equal to 1, and you try to eliminate two constants in each step to find the other constant

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Thankyouuuuu I had been hopeless the entire day becuz of partial fraction and this vid literally saved my life

[@SkanCityAcademy_SirJohn]

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@@SkanCityAcademy_SirJohn I found you when I searched partial fractions with quadratic factors

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[@SkanCityAcademy_SirJohn]

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Is this method always correct?

[@SkanCityAcademy_SirJohn]

Yes, except that the question type is different

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[@SkanCityAcademy_SirJohn]

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[@SkanCityAcademy_SirJohn]

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Thanks for watching

[@IllustriousProfessional]

it was really helpful❤

[@SkanCityAcademy_SirJohn]

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[@PortiaAuntie-rt2dd]

Please what if the numerator is not a quadratic equation

[@SkanCityAcademy_SirJohn]

Kindly explain further, do you mean if you have an improper fraction?

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[@SkanCityAcademy_SirJohn]

You are most welcome. Thanks for watching as well

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[@SkanCityAcademy_SirJohn]

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[@osasuruth1207]

Sir what about this question 2x^2+3x+10/(x+1)(x+2)

[@SkanCityAcademy_SirJohn]

For this question, you will use the improper fraction method.
After the long division you will get
2 + (-3x + 6)/(x+1)(x+2)
Hence you work of the term on the right hand side
A /( x+ 1) + B / (x + 2).
You will get A = 9 and B = -12.
Finally you have the decomposition to be
2 + 9/(x+1) - 12/(x+2)
Sorry for the late reply

[@osasuruth1207]

Thank you and there's no problem sir

[@SkanCityAcademy_SirJohn]

@osasuruth1207 you are welcome, which school do you attend?

[@nolanminev2064]

How do you even get 5x^2-3x+4 it seems so out of nowhere like he just wrote it down and I couldn’t follow

[@SkanCityAcademy_SirJohn]

Can you explain further ?

[@samisamby8044]

it's the numerator of the original function that he chose for the example.

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[@SkanCityAcademy_SirJohn]

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[@user-il9wn7rl3j]

7:01 can somebody explain why it's -2 instead of 2? Bcs earlier he puts x equal to 2???

[@SkanCityAcademy_SirJohn]

In finding the value of c, we want to compare coefficient of x, we have expressions with x attached as ' Cx - 2Bx' = -3x.
From the LHS, coeefifcent of x is -2B, that's where the negative comes from.

[@aadik07]

Why are you making it harder and explaining it ??? We can take X= 0 and find C ? LOL

[@SkanCityAcademy_SirJohn]

Thanks for your contribution.

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[@SkanCityAcademy_SirJohn]

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