(5x^3 -x^2+8x -55)/(x^4 +5x^3+11x^2)
decompose into partial functions...please help?

- anonymous

(5x^3 -x^2+8x -55)/(x^4 +5x^3+11x^2)
decompose into partial functions...please help?

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- dinamix

(5x^3-x^2+8x-55)/x(x^3+5x^2+11x) @hailbug i help u bit

- anonymous

would I only be factoring one x from the denominator or x^2?

- dinamix

no thats only u have thing little dude

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## More answers

- anonymous

what? sorry I'm confused

- anonymous

@hailbug why do need to decompose into partial functions?

- anonymous

its part of my summer calc homework. i've searched every tutorial for this but I literally can't find anything that closely resembles this. I was hoping someone would help me out

- dinamix

@hailbug u have use Euclidean division thats only

- anonymous

@hailbug do need solution or answer?

- anonymous

@ASAAD123 solution

- anonymous

you need to start by factoring the whole denominator. The common denominator is x², so it's
\[\frac{ 5x^3-x^2+8x-55 }{ x^2(x^2+5x+11) }\]
Both of those are quadratic so you can use\(\frac{ Ax+B }{ ax^2+bx+c }\) as a guess.
\[\frac{ 5x^3-x^2+8x-55 }{ x^2(x^2+5x+11) }=\frac{ Ax+B }{ x^2 }+\frac{ Cx+D }{ x^2+5x+11 }\]

- dinamix

@peachpi yes this is the anwer

- anonymous

for a full table
http://tutorial.math.lamar.edu/Classes/CalcII/PartialFractions.aspx

- anonymous

It's not the answer, just a guess at the format. You still have to multiply, solve the system, etc to get the coefficients

- anonymous

thank you so much that makes so much sense. I was trying to factor everything thinking that was the answer

- dinamix

i want ask u qustion how did u know degree of Numerator is Ax+B and cx+D not only D or ax^2 +cx+d ? @peachpi

- freckles

the numerator should be at least one degree less than the denominator @dinamix

- dinamix

cuz i like your method but i use only (euclidean division ) i want learn other method @peachpi @freckles

- freckles

So if the denominator is 2nd degree, then new numerator choice should be something like Ax+B since this will also include B since A can be zero still (which means the degree of the numerator will be either 0 or 1).

- dinamix

@freckles ty so much

- anonymous

##### 1 Attachment

- anonymous

@peachpi so I got the answer \[((3x - 5)/x^2)+ ((2x-11)/x^2 +5x +11) \] is this correct?

- anonymous

oh haha @ASAAD123 didn't see that, sorry

- anonymous

\[\frac{ -5 }{ x^2 }+\frac{ 3 }{ x }+\frac{ 2x-11 }{ x^2+5x+11 }\]

- anonymous

@hailbug correct

- dinamix

denominator is degree 4 not 5 @ASAAD123

- dinamix

u make mistake

- anonymous

@dinamix where is that mistake?

- anonymous

yes that's correct @ASAAD123

- dinamix

its ax+d/x^2 + bx+c/x^2+5x+11

- anonymous

the denominator is still degree 4. You can split that first one up and then the denominator will reduce to x.
|dw:1440868401732:dw|

- dinamix

hmm ok

- anonymous

basically, you need to look at the degree of the least common denominator, not the sum of the individual degrees

- dinamix

ok i understand know , ty

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