Final answer:
The expression 9x^2-6x-24 is factored into (3x - 8)(3x + 3) using the Leading Coefficient method.
Step-by-step explanation:
To factor the expression 9x² - 6x - 24 using the Leading Coefficient method, we need to find two numbers whose product is equal to the product of the leading coefficient (9) and the constant term (-24) and whose sum is equal to the coefficient of the linear term (-6).
Let's write down the factors for 9 and -24:
9 can be factored as 1 × 9 or 3 × 3.
-24 can be factored as 1 × -24, -1 × 24, 2 × -12, -2 × 12, 3 × -8, -3 × 8, 4 × -6, or -4 × 6.
We can see that the factors 3 and -8 satisfy both conditions.
Therefore, we can factor the expression as (3x - 8)(3x + 3).