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check whether p(x) is a multiple of g(x) or not where p(x)=x^3-x+1, g(x)=2-3x

$Given p (x) = x^{3} - x + 1 g (x) = 3 - 2 x 2 - 3 x = 0 \Rightarrow x = \frac{2}{3} p (\frac{2}{3}) should be 0 if p(x) must be a multiple of g(x) \Rightarrow (\frac{2}{3})^{2} - \frac{2}{3} + 1 \Rightarrow \frac{8}{27} - \frac{2}{3} + 1 \Rightarrow \frac{8 - 18 + 27}{27} \Rightarrow \frac{17}{27} \neq 0 So p(x) is not a multiple of g(x)$

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