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Please tell me if this does what you want:

poly[n_Integer?Positive] :=
 {
   Array[{{Hold[c][#], #}, # - 1, # + 1} &, n + 1, 0],
   Sum[Hold[c][i] Hold[x]^i, {i, 0, n}]
 } /. {{var__}, expr_} :>
   ReleaseHold[
    Hold[Manipulate][Hold[Plot][expr, {Hold[x], 0, 1}], var]
   ]

poly[4]

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