1. **State the problem:** Find the limit $$\lim_{x \to -\infty} \left(1 + (x^2 - 1)e^{-x}\right).$$\n\n2. **Recall the behavior of terms:** As $x \to -\infty$, $x^2$ grows very large positively, and $e^{-x} = e^{|x|}$ grows very large positively because $-x$ becomes very large positive.\n\n3. **Analyze the term $(x^2 - 1)e^{-x}$:** Since $x^2 - 1 \approx x^2$ for large $|x|$, and $e^{-x}$ grows exponentially, the product $(x^2 - 1)e^{-x}$ behaves like $x^2 e^{|x|}$ which tends to $+\infty$.\n\n4. **Combine terms:** The expression inside the limit is $1 + (x^2 - 1)e^{-x}$. Since $(x^2 - 1)e^{-x} \to +\infty$, the whole expression tends to $+\infty$.\n\n**Final answer:** $$\lim_{x \to -\infty} \left(1 + (x^2 - 1)e^{-x}\right) = +\infty.$$