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------------------------------------------------ Factor the following expression:

\[ 8x^3 - 48x^2 - 216x \]

The factored form of the expression 8x³-48x²-216x is 8x(x - 9)(x + 3), which is achieved by first finding the greatest common factor (8x) and then factoring the remaining quadratic.

Explanation:

In factoring the expression 8x³-48x²-216x, first we need to find the greatest common factor (GCF) in the terms. In this case, the GCF is 8x. When we divide each term by 8x, we are left with x² - 6x - 27. Now we have 8x(x² - 6x - 27).

Next, we factor the quadratic x² - 6x - 27. This factors to (x - 9)(x + 3), because -9 and 3 add up to -6 (the coefficient of x) and multiply to -27 (the constant term). Therefore, the fully factored form of the expression is 8x(x - 9)(x + 3)

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