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C2 problem please help

Find the polynomial in x of the third degree, which vanishe when x=-1 and x=2, has the value 8 when x=0 and leaves the remainder 16/3 when divided by 3x+2

My working is attached

I need help as I think i am going down the wrong direction

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Reply 1
Haven't checked it but it may be easier to consider (x+1)(x-2)(ax+b) where b is easy to fine and a will follow after that.

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