Answer:
I think there might be a typo in your expression - you have both 2x^2 and -3x^2. Assuming you meant 2x^2 - 3x - 4, here's how to find the quotient and remainder when dividing by x - 2:
First, set up the long division problem like this:
markdown
2x - 7
___________
x - 2 | 2x^2 - 3x - 4
Divide 2x^2 by x to get 2x as the first term in the quotient. Then multiply x - 2 by 2x to get 2x^2 - 4x, and subtract that from the original expression:
lua
2x - 7
___________
x - 2 | 2x^2 - 3x - 4
- (2x^2 - 4x)
-----------
x - 4
Now we have a remainder of x - 4. So the quotient is 2x - 7 and the remainder is (2)(2)^2 - 3(2) - 4 = -4.
Therefore, P(2) = -4.