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

QUESTION POSTED AT 01/06/2020 - 03:24 PM

QUESTION POSTED AT 01/06/2020 - 03:24 PM

Let . We want to find the least such that has remainder 0 when divided by .

By the polynomial remainder theorem, this will happen if when :

We can check this:

By the polynomial remainder theorem, this will happen if when :

We can check this:

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