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math:partial_fraction_decomposition [2020/11/13 15:28] – created epixmath:partial_fraction_decomposition [2020/12/13 22:05] (current) – [Factor Decomposition Table] epix
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 ===== Factor Decomposition Table ===== ===== Factor Decomposition Table =====
-{{:math:2020-11-13-091051_601x468_scrot.png|}} Unfortunately this must be memorized :/+{{:math:2020-11-13-091051_601x468_scrot.png|}}
  
 +Unfortunately this must be memorized :/
 +
 +Note: Terms like $x^2$ are __Squared Linears__
 ===== Steps ===== ===== Steps =====
 ==== Step 0: Divide Function ==== ==== Step 0: Divide Function ====
-Only do this if the numerator's degree is higher than the denominator's. Use [[math:polynomial_division|Polynomial Division]] to divide the function. PFD can be used on the remainder as the degrees should be acceptable for PFD.+Only do this if the numerator's degree is greater than or equal to the denominator's. Use [[math:polynomial_division|Polynomial Division]] to divide the function. PFD can be used on the remainder as the degrees should be acceptable for PFD.
  
 ==== Step 1: Factor Denominator ==== ==== Step 1: Factor Denominator ====
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 ==== Step 3: Solving for Constants ==== ==== Step 3: Solving for Constants ====
-To solve for A, B, C, ... Z, first you must add together all terms of the PFD. This means finding a common denominator. Afterwards, you can drop the denominator and group all terms by degree of x. By doing this, you can create a system of equations for constants that share a common factor (i.e. x^2 or x). Constants without a variable are grouped into one aswell((think of them as x^0)). The sum of the grouped constants is equal to the coefficient of the term with the common factor from the original function. There should be enough equations to solve for all constants present in the PFD. +To solve for A, B, C, ... Z, first you must add together all terms of the PFD. This means finding a common denominator. Afterwards, you can drop the denominator, distribute the constants in, and group all terms by degree of x. By doing this, you can create a system of equations for constants that share a common factor (i.e. x^2 or x). Constants without a variable are grouped into one aswell((think of them as x^0)). The sum of the grouped constants is equal to the coefficient of the term with the common factor from the original function. There should be enough equations to solve for all constants present in the PFD.
 ==== Step 4: Substituting for Solution ==== ==== Step 4: Substituting for Solution ====
 Return back to the answer of Step 2. You can substitute the constants with the solutions from Step 3 for the answer. Return back to the answer of Step 2. You can substitute the constants with the solutions from Step 3 for the answer.

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