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Question

The expression 2x3+bx2cx+d leaves the same remainder, when divided by x+1 or x2 or 2x1. Find b and c.

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Solution

(x+1)(x2)(2x1)=2x3+bx2cx+d
(x22x+x2)(2x1)=2x3+bx2cx+d
(x2x2)(2x1)=2x3+bx2cx+d
2x3x22x2+x4x+2=2x3+bx2cx+d
2x33x23x+2=2x3+bx2cx+d
Comparing the coefficients, we get
b=3,c=3,d=2
b=3,c=3,d=2

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