Express x^ 3 -4 (x-1)(x+2) in the form S(x)+ A x-1 + B x+2

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Express x3−4(x−1)(x+2)\frac{x^{3}-4}{(x-1)(x+2)} in the form S(x)+Ax−1+Bx+2,S(x)+\frac{A}{x-1}+\frac{B}{x+2}, where S(x)S(x) is a polynomial. Find S(x)S(x), AA and BB.

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