Partial Fraction Decomposition

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SUMMARY

The discussion centers on the process of Partial Fraction Decomposition for the rational function \(\frac{4x^{4}-8x^{3}+5x^{2}-2x-1}{2x^{2}-3x-2}\). The user correctly factored the denominator into \((2x+1)(x-2)\) but initially struggled with the setup of the decomposition. After realizing the need to perform polynomial long division to ensure the degree of the numerator is less than that of the denominator, the user successfully completed the problem. This highlights the importance of proper setup in Partial Fraction Decomposition.

PREREQUISITES
  • Understanding of polynomial long division
  • Familiarity with factoring polynomials
  • Knowledge of Partial Fraction Decomposition techniques
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study polynomial long division methods in detail
  • Practice factoring complex polynomials
  • Explore advanced techniques in Partial Fraction Decomposition
  • Learn about applications of Partial Fraction Decomposition in integral calculus
USEFUL FOR

Students studying algebra, particularly those learning about rational functions and Partial Fraction Decomposition, as well as educators looking for examples to illustrate these concepts.

protivakid
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Homework Statement



[tex]\frac{4x^{4}-8x^{3}+5x^{2}-2x-1}{2x^{2}-3x-2}[/tex]

Homework Equations





The Attempt at a Solution



I started of by breaking the bottom part down into (2x+1)(x-2) which then allowed me to set...
[tex]\frac{A}{(2x+1)}[/tex]+[tex]\frac{B}{(x-2)}[/tex]

The problem is from here I tried synthetic division however it gave me an answer that did not make any sense. Am I setting this up right or have I messed up already? Thanks guys.
 
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I don't know if you forgot to include the step of dividing the polynomial fraction such that the degree of the numerator polynomial is less than that of the denominator's.
 
Thanks for the reply, I didn't forget to put it in, I forgot to do it lol. I'm still learning how to do all these problems so even obvious hints make a world of difference to me. I managed to completely solve it from there so thank you.
 

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