## anonymous one year ago I'll FAN & MEDAL just please help!!! The smallest integer that can be added to -2m3 − m + m2 + 1 to make it completely divisible by m + 1 is

1. freckles

so we want the remainder to be 0 that is when we plug in -1 (we are pluggin in -1 because we are dividing by m-(-1))

2. freckles

hey is your thingy really $-2m^3-m+m^2+1$?

3. anonymous

is this where synthetic division comes in?

4. anonymous

Yes

5. freckles

you could use syntheic or easier just plug in -1 into that thing and then see what you need to add to it to make it 0

6. freckles

$-2(-1)^3-(-1)+(-1)^2+1 \text{ plus what gives you 0 }$

7. freckles

it might help to simplify the first part first :)

8. anonymous

i got 3

9. freckles

after simplifying $2(-1)^3-(-1)+(-1)^2+1?$

10. anonymous

wait -2

11. anonymous

i used my calculator

12. freckles

$-2m^3-m+m^2+1 \\ \text{ plug in } -1 \text{ since we have that we are dividing by } m-(-1) \\ -2(-1)^3-(-1)+(-1)^2+1$ $(-1)^3=(-1)(-1)(-1)=(1)(-1)=-1 \\ \text{ and } \\ (-1)^2=(-1)(-1)=1 \\ \text{ so you really have } -2(-1)-(-1)+1+1 \\ \text{ and we also know } -2(-1)=2 \text{ and } -(-1)=+1 \\ \text{ so we have } 2+1+1+1$

13. freckles

2+3 should be 5 then you need to figure out what you can add to 5 that will give you 0

14. anonymous

5+-5=0

15. freckles

yes so the answer should be -5 that is $-2m^3-m+m^2+1+(-5) \text{ divided by } m+1 \text{ should give a remainder of } 0$ it having a remainder of 0 means that one thing is divisible by (m+1)

16. freckles

http://www.wolframalpha.com/input/?i=what+is+the+remainder+of+%28-2m%5E3-m%2Bm%5E2%2B1-5%29%2F%28m%2B1%29 and as you see here the remainder is 0 which is just what we wanted

17. anonymous

Thank you, i understand it now