1. **State the problem:** Simplify the quadratic expression $6x^2 - 30x + 24$ by factoring. 2. **Formula and rules:** To factor a quadratic expression, first find the greatest common factor (GCF) of all terms. 3. **Find the GCF:** The coefficients are 6, -30, and 24. The GCF of 6, 30, and 24 is 6. 4. **Factor out the GCF:** $$6x^2 - 30x + 24 = 6(x^2 - 5x + 4)$$ 5. **Factor the quadratic inside the parentheses:** Find two numbers that multiply to $4$ and add to $-5$. These numbers are $-4$ and $-1$. 6. **Write the factored form:** $$6(x^2 - 5x + 4) = 6(x - 4)(x - 1)$$ 7. **Final answer:** The factored form of $6x^2 - 30x + 24$ is $$6(x - 4)(x - 1)$$