1.

Which of the following should be added to `9x^(3)+6x^(2)+x+2`, so that the sum is divisible by `(3x+1)`?A. `-4`B. `-3`C. `-2`D. `-1`

Answer» Correct Answer - C
Let k should be added to the given expression so that the sum is divisible by `(3x+1)`.
Let `f(x)=9x^(3)+6x^(2)+x+2+k`
Given , `f(-(1)/(3))=0`
`rArr9(-(1)/(3))+6(-(1)/(3))^(2)-(1)/(3)+2+k=0`
`rArr-(1)/(3)+(2)/(3)-(1)/(3)+2+k+0rArr2+k=0`
`rArrk=-2`.


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