1. **State the problem:** Simplify or factor the quadratic expression $6x^2 - 30x + 24$. 2. **Identify the greatest common factor (GCF):** The coefficients 6, -30, and 24 share a GCF of 6. 3. **Factor out the GCF:** $$6x^2 - 30x + 24 = 6(x^2 - 5x + 4)$$ 4. **Factor the quadratic inside the parentheses:** Find two numbers that multiply to $4$ and add to $-5$. These numbers are $-4$ and $-1$. 5. **Write the factored form:** $$6(x^2 - 5x + 4) = 6(x - 4)(x - 1)$$ 6. **Final answer:** The factored form of $6x^2 - 30x + 24$ is $$6(x - 4)(x - 1)$$