Question

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

Answer 1

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))

Answer 2

hey is your thingy really
\[-2m^3-m+m^2+1\]?

Answer 3

is this where synthetic division comes in?

Answer 4

Yes

Answer 5

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

Answer 6

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

Answer 7

it might help to simplify the first part first :)

Answer 8

i got 3

Answer 9

after simplifying
\[2(-1)^3-(-1)+(-1)^2+1?\]

Answer 10

wait -2

Answer 11

i used my calculator

Answer 12

\[-2m^3-m+m^2+1 \\ \text{ plug in } -1 \text{ since we have that we are dividing by } m-(-1) \\ -2(-1)^3-(-1)+(-1)^2+1\]

\[(-1)^3=(-1)(-1)(-1)=(1)(-1)=-1 \\ \text{ and } \\ (-1)^2=(-1)(-1)=1 \\ \text{ so you
really have } -2(-1)-(-1)+1+1 \\ \text{ and we also know } -2(-1)=2 \text{ and } -(-1)=+1 \\ \text{ so we have } 2+1+1+1\]

Answer 13

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

Answer 14

5+-5=0

Answer 15

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)

Answer 16

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

Answer 17

Thank you, i understand it now