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Question

Using the remainder theorem, find the remainder, when p(x) is divided by g(x), where
p(x)=2x39x2+x+15,g(x)=2x3

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Solution

p(x)=2x39x2+x+15g(x)=2x3

By remainder theorem, when p(x) is divided by ( 2x − 3), then the remainder = p(32).

Putting x = 3 in p(x), we get

p(32)=2(32)39(32)2+(32)+15=274814+32+15=544+64+604=54+6+604=124=3

∴ Remainder = 3

Thus, the remainder when p(x) is divided by g(x) is 3.


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