1. State the problem: Factor $x^2$. 2. Recognize that $x^2$ is a perfect square and can be written as $x \cdot x$. 3. Factor by extracting the common factor $x$ to get $x(x)$. 4. Check the result by expanding $x(x)$ to obtain $x^2$, confirming the factorization. Final answer: $x^2 = x(x)$.