For the denominator

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

For the denominator x(x−2)2(x2+4)x(x-2)^{2}(x^{2}+4), the correct general decomposition is (a) Ax+B(x−2)2+Cx+Dx2+4\dfrac{A}{x}+\dfrac{B}{(x-2)^{2}}+\dfrac{Cx+D}{x^{2}+4} (b) Ax+Bx+Cx−2+Dx2+4\dfrac{A}{x}+\dfrac{Bx+C}{x-2}+\dfrac{D}{x^{2}+4} (c) Ax+Bx−2+C(x−2)2+Dx+Ex2+4\dfrac{A}{x}+\dfrac{B}{x-2}+\dfrac{C}{(x-2)^{2}}+\dfrac{Dx+E}{x^{2}+4} (d) Ax+Bx−2+C(x−2)2+Dx2+4\dfrac{A}{x}+\dfrac{B}{x-2}+\dfrac{C}{(x-2)^{2}}+\dfrac{D}{x^{2}+4}

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