1. **State the problem:** Simplify or analyze the expression $4x^2 + x$. 2. **Identify the terms:** The expression consists of two terms: $4x^2$ and $x$. 3. **Factor the expression:** We can factor out the common factor $x$ from both terms. $$4x^2 + x = x(4x + 1)$$ 4. **Explanation:** Factoring helps to simplify expressions and solve equations more easily by breaking them into products. 5. **Final answer:** The factored form of the expression is $$x(4x + 1)$$.