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設 f(x)為多項式 deg f(x)>3,若f(x) 之常數項為2,且f(x)除以(x-2)(c+1)的餘式為2x-6,
則 f(x) 除以x(x-2)(c+1)的餘式為
O

Answer 1

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綾

f(x) = (x-2)(x+1)q(x) + (2x-6)
f(0) = (-2)(1)q(0) + (-6) = 2
=> q(0) = -4
所以q(x)可以化成x(g(x)) -4
得f(x) = (x-2)(x+1)[x(g(x)) -4] + (2x-6)
= x(x-2)(x+1)g(x) -4(x-2)(x+1) + (2x-6)
故f(x)除以x(x-2)(x+1)的餘式為
-4(x-2)(x+1) + (2x-6) = -4*x^2 + 6x + 2