Factor completely 2x^2+22x-24

To factor completely the expression 2x^2 + 22x - 24, we can look for two numbers that multiply to give -48 (the product of the first and last coefficients) and add to give 22 (the middle coefficient).

The numbers that satisfy these conditions are 24 and -2.

We can then rewrite the expression as follows:

2x^2 + 24x - 2x - 24

Now, we group common factors:

(2x^2 + 24x) - (2x + 24)

Next, we factor out the greatest common factor from each group:

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

Notice that we have a common factor, (x + 12), which we can factor out:

2(x + 12)(x - 1)

Therefore, the expression 2x^2 + 22x - 24 completely factors to 2(x + 12)(x - 1).