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

Answer 1

interpretation:
the division must be excact, that is,
there cannot be a remainder.

Arrange the terms in the proper order and do a synthetic division:

-1 | -2 1 -1 1
....... 2..-3..4
.... -2 3..-4..5

so we should have had a 0 instead of a 5 at the end of our algorithm, that means the constant at the end of our function should have been -4
But we had a 1, so adding -5 would have done the trick