Question

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

Are you comfortable with synthetic divison or long division?

Answer 2

it doesnt matter haha

Answer 3

Okay, making sure. So let's divide -2m^3 +m^2 -m +1 by m+1 and see what we get. Ill use synthetic.



So this division gives us:
\[-2m^{2} + 3m -4 + \frac{ 5 }{ m+1 }\]
So what this means is as long as 5/(m+1) reduces, we're good. Since we're allowed to use any integer, we can make m = -6