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Algebra 2SuperchallengeRational Expressions & Functions

Rational Expressions & Functions · Superchallenge problem

Constants A,B,C,DA, B, C, D satisfy

1(x−1)(x−2)(x−3)(x−4)=Ax−1+Bx−2+Cx−3+Dx−4\dfrac{1}{(x - 1)(x - 2)(x - 3)(x - 4)} = \dfrac{A}{x - 1} + \dfrac{B}{x - 2} + \dfrac{C}{x - 3} + \dfrac{D}{x - 4}

for all xx other than 1,2,3,41, 2, 3, 4. Find A+16B+81C+256DA + 16B + 81C + 256D.