Factor completely 2x^3+22x^2-24x
To factor the expression 2x^3 + 22x^2 - 24x, we can first factor out the greatest common factor, which is 2x:
2x(x^2 + 11x - 12)
Next, we can factor the quadratic expression inside the parentheses. We need to find two numbers that multiply to -12 (the constant term) and add up to 11 (the coefficient of the x term). These numbers are 12 and -1:
2x(x + 12)(x - 1)
Therefore, the completely factored form of the expression is 2x(x + 12)(x - 1).