Determine m if the polynomial P is divisible by x-3. P=x^3+mx^2+3mx-9

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P= x^3 + mx^2 + 3mx -9

P is dividible by (x-3)

Then (x-3) is one of P's factors, and 3 is one of the roots for P.

==> P(x) = (x-3)*Q(x)

==> P(3) = 0

P(3) = 3^3 + m(3^2) + 3m(3) - 9 = 0

==> 27 + 9m + 9m - 9 = 0

==> 18 + 18m = 0

==> 18m = -18

==> m = -1

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