Polynomials, Cubic Equations and Partial Fractions - Comparing Coefficients in Polynomial Identities

Polynomials, Cubic Equations and Partial Fractions - Comparing Coefficients in Polynomial Identities

TGM Original Questions

Given that \(4{{x}^{3}}+6{{x}^{2}}+3x-2=\left( Cx+2 \right)\left( x-2 \right)\left( x+3 \right)+Dx+E\) holds for all real values of \(x\), find the values of \(C\), \(D\) and \(E\).

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Answer:\(C = 4\), \(D = 25\) and \(E = 10\)

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