1. **State the problem:** Simplify the expression $4x - 2x^2 - 2$ or rewrite it in a standard polynomial form. 2. **Rewrite the expression:** The given expression is $4x - 2x^2 - 2$. 3. **Arrange terms in descending powers of $x$:** $$-2x^2 + 4x - 2$$ 4. **Factor if possible:** We can factor out $-2$: $$-2x^2 + 4x - 2 = -2(x^2 - 2x + 1)$$ 5. **Recognize the perfect square:** $$x^2 - 2x + 1 = (x - 1)^2$$ 6. **Final factored form:** $$-2(x - 1)^2$$ **Answer:** The expression $4x - 2x^2 - 2$ can be rewritten as $$-2(x - 1)^2$$.