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Question

The polynomials (2x3+x2ax+2) and (2x33x23x+a) when divided by (x -2) leave the same remainder. Find the value of a.

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Solution

f(x)=2x3+x2ax+2g(x)=2x33x23x+aBy remainder theorem, when f(x) is divided by x-2, then the remainder = f(2)Put x=2 in f(x), we get,f(2)=2(2)3+(2)2a(2)+216+42a+2=2a+22By remainder theorem, when g(x) is divided by x-2, then the remainder = g(2)Put x=2 in g(x), we get,g(2)=2(2)33(2)23(2)+a16126+a=2+aIts is given that,f(2)=g(2)2a+22=2+a3a=24a=8

The value of a is 8


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