Question

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

please help !

Answer 1

Let

f(m) = -2m^3 - m + m^2 + 1

Answer 2

if f(m) were divisible by m+1, then f(-1) would be 0 due to the remainder theorem

Answer 3

what is f(-1) equal to in this case?

Answer 4

If you aren't sure, then...

f(m) = -2m^3 - m + m^2 + 1

f(-1) = -2(-1)^3 - (-1) + (-1)^2 + 1 ... replace every m with -1

f(-1) = ???