Why the answer is A, and why the others tempt you.
Apply the product rule $\dfrac{d}{dx}(uv) = u'v + uv'$ with $u = x^2$ and $v = e^x$: $2x e^x + x^2 e^x = x e^x (2 + x)$. Differentiating only the $x^2$ factor gives $2x e^x$, which is incomplete.
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