The discussion focuses on the process of partial fraction decomposition for the expression (x^4 - 2x^3 + x^2 + 2x - 1) / (x^2 - 2x + 1). The user correctly performed polynomial long division, resulting in x^2 + (2x - 1) / (x^2 - 2x + 1). However, the partial fraction decomposition is incomplete as the denominator factors into (x - 1)(x - 1), indicating the need for further expansion. The correct form should include the coefficients A and B for the terms associated with the factors.
PREREQUISITESStudents studying algebra, particularly those tackling polynomial expressions and partial fraction decomposition, as well as educators seeking to reinforce these concepts in their curriculum.
Jbreezy said:Homework Statement
Write out the form of the partial fraction decomposition of not determine the numerical values of the coefficients.
Homework Equations
x^4 -2x^3 + x^2 +2x -1 / x^2 -2x +1
The Attempt at a Solution
I did the division and I got x^2 + ((2x-1)) / (x^2 -2x +1)
So I took
((2x-1)) / (x^2 -2x +1) = Ax + B / x^2 -2x +1
Is this right? It has been forever since I did these.