Factor completely.2, x, cubed, plus, 22, x, squared, minus, 24, x2x 3 +22x 2 −24x

The expression you provided is 2x^3 + 22x^2 - 24x. Here's how to factor it completely:

Step 1: First, look for the greatest common factor (GCF) in all terms. In this case, the GCF is 2x. So, factor out 2x from each term:

2x(x^2 + 11x - 12)

Step 2: Now, look at the quadratic inside the parentheses. It can be factored further. Look for two numbers that multiply to -12 (the constant term) and add to 11 (the coefficient of the x term). The numbers 12 and -1 fit these conditions. So, factor the quadratic:

2x(x - 1)(x + 12)

So, the completely factored form of the expression 2x^3 + 22x^2 - 24x is 2x(x - 1)(x + 12).