Question

(5x^3 -x^2+8x -55)/(x^4 +5x^3+11x^2)

decompose into partial functions...please help?

Answer 1

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

Answer 2

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

Answer 3

no thats only u have thing little dude

Answer 4

what? sorry I'm confused

Answer 5

@hailbug why do need to decompose into partial functions?

Answer 6

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

Answer 7

@hailbug u have use Euclidean division thats only

Answer 8

@hailbug do need solution or answer?

Answer 9

@ASAAD123 solution

Answer 10

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.
\[\frac{ 5x^3-x^2+8x-55 }{ x^2(x^2+5x+11) }=\frac{ Ax+B }{ x^2 }+\frac{ Cx+D }{ x^2+5x+11 }\]

Answer 11

@peachpi yes this is the anwer

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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).

Answer 19

@freckles ty so much

Answer 20

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

Answer 21

oh haha @ASAAD123 didn't see that, sorry

Answer 22

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

Answer 23

@hailbug correct

Answer 24

denominator is degree 4 not 5 @ASAAD123

Answer 25

u make mistake

Answer 26

@dinamix where is that mistake?

Answer 27

yes that's correct @ASAAD123

Answer 28

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

Answer 29

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