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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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`p(x)=2x^3+ax^2+11x+a+3`
divisible by `(2x+1)`
`2x-1=0`
`x=1/2`
putting ,`x=1/2`
`p(x)=2x^3+ax^2+11x+a+3`
`p(1/2)=2(1/2)^3+a(1/2)^2+11(1/2)+a+3`
`0=2xx1/8+axx1/4+11/2+a+3`
`0=1/4+a/4+11/2+a+3`
`0=(1+a+22+4a+12)/(4)`
`0=(5a+35)/4`
`0xx4=5a+35`
`0=5a+35`
`-5a=35`
`a=1/5xx(-35)`
`a=-7`
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