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

The expression you provided seems to have a typo. It should probably be "2x^2 + 3x - 2". Let's factor this expression.

Step 1: Identify the coefficients of the quadratic equation. Here, a = 2, b = 3, and c = -2.

Step 2: Find two numbers that multiply to give ac (which is -4 in this case) and add up to b (which is 3 in this case). The numbers that satisfy these conditions are 4 and -1 because 4*-1 = -4 and 4 + -1 = 3.

Step 3: Rewrite the middle term of the quadratic equation as the sum of the terms 4x and -x. This gives us 2x^2 + 4x - x - 2.

Step 4: Factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together. This gives us 2x(x + 2) - 1(x + 2).

Step 5: Notice that (x + 2) is a common factor. We can factor out this term to get (2x - 1)(x + 2).

So, the expression 2x^2 + 3x - 2 factors to (2x - 1)(x + 2).