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For what values of a is 2x^3+a x^2+11 x+...

For what values of `a` is `2x^3+a x^2+11 x+a+3` exactly divisible by `(2x-1)?`

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`f(x)=2x^3+ax^2+11x+a+3`
When `2x^3+ax^2+11x+a+3` exactly divisible by `(2x-1)` then `(2x-1)` must be factor.
`(2x-1)=x=1/2`
Now,
Put `x=1/2` in `f(x)`
`=>2(1/2)^3+a(1/2)^2+11(1/2)+a+3=0`
`=>1/4+a/4+11/2+a+3=0`
`=>5a/4+35/4=0`
`=>5a+35=0`
`=>a=-7`
`therefore` The value of `a=-7`
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