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The given function $$f(x) = 2x^4 - 6x^3 + 3x^2 + 3x - 2$$ is not divisible by $$g(x)$$, where the function $$g(x)$$ is
We have $$f(1) = 2 - 6 + 3 + 3 - 2 = 0$$ and $$f(2) = 32 - 48 + 12 + 6 - 2 = 0$$, so $$(x - 1)$$, $$(x - 2)$$ and their product $$x^2 - 3x + 2$$ divide f. Dividing gives $$f(x) = (x - 1)(x - 2)(2x^2 - 1)$$. The factor $$x^2 - 2x + 2$$ does not appear, so f is not divisible by $$x^2 - 2x + 2$$.
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