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Using the remainder theorem , find the r...

Using the remainder theorem , find the remainder , when `p (x)` is divided by `g (x)`, where
`p(x)=2x^(3)-9x^(2)+x+15 , \ g(x)=2x-3`.

Text Solution

Verified by Experts

The correct Answer is:
3
`g(x)=0rArr2x-3=0rArr2x=3rArrx=(3)/(2)`.
Remainder is `p((3)/(2))={2xx((3)/(2))^(3)-9xx((3)/(2))+(3)/(2)=15}`
`=((27)/(4)-(81)/(4)+(3)/(2)+15)=((27-81+6+60)/(40))=(12)/(4)=3`.
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