You can put this solution on YOUR website! The problem gives you:
P(x)/(x-2) = 2x^2+x-2+-5/(x-2)
P(x)/(x-2) = 2x^2+x-2 + -5/(x-2)
.
If you multiply BOTH sides by (x-2), the (x-2) cancels from both sides leaving you with your answer:
P(x) = (x-2)(2x^2+x-2) + -5
.
At this point, you should "expand" the left term:
P(x) = (2x^3+x^2-2x)-(4x^2+2x-4) + -5
P(x) = 2x^3+x^2-2x-4x^2-2x+4 + -5
P(x) = 2x^3-3x^2-4x+4 + -5
P(x) = 2x^3-3x^2-4x-1
