Show that if the pol. p(x) is divisible by (ax+b)^2, then p'(x) is divisible by (ax + b)^(n-1) where n > 1

A polynomial f(x) to be divisible by another polynomial g(x), there should be another polynomial s(x), s.t f(x) = g(x)s(x)

Now my p(x) = (ax+b)^n-1 s(x)

then my p'(x) = ((ax+b)^n)' s(x) + ((ax+b)^n) (s(x))'

p'(x) = n(ax+b)^(n-1) * (ax + b)' s(x) + ((ax+b)^n) (s(x))

p'(x) = n(ax+b)^(n-1) * a * s(x) + ((ax+b)^n) (s(x))

but I do not know how to proceed anymore? Can anybody give me a hint? And about the s(x), should I leave the s(x) just like this or I have to give an expression (value) to it?

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