The smallest integer that can be added to -2m^3-m+m^2+1 to make it completely divisible by m+1 is

We can use the polynomial remainder theorem here. will be exactly divisible by if the remainder upon division of it by is 0. The PRT says that this remainder is exactly equal to the value of the polynomial when . We have



Since the remainder is 5, that's how much we should subtract from the original polynomial. So the integer that we need to add is -5.

To confirm: by the PRT, the remainder should be 0. We get

He is right i did this thing before