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Question

If x4(xa)(xb)(xc)=P(x)+Axa+Bxb+Cxc then P (x) =

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Solution

(xa)(xb)(xc)=[x2(a+b)x+ab](xc)
=x2cx2(a+b)x2+c(a+b)x+abxabc
(xa)(xb)(xc)=x3(a+b+c)x2+(ab+bc+ca)xabc

x4(xa)(xb)(xc)=P(x)+Axa+Axb+Cxcx4=P(x)(xa)(xb)(xc)+A(xb)(xc)+B(xa)(x5)+C(x+a)(xb)
Dividend = Quotient × Divisor + Remainder
P(x) = Quotient
P(x) = x+a+b+c

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