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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

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  1. freckles
    • one year ago
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    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
    • one year ago
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    hey is your thingy really \[-2m^3-m+m^2+1\]?

  3. anonymous
    • one year ago
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    is this where synthetic division comes in?

  4. anonymous
    • one year ago
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    Yes

  5. freckles
    • one year ago
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    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
    • one year ago
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    \[-2(-1)^3-(-1)+(-1)^2+1 \text{ plus what gives you 0 }\]

  7. freckles
    • one year ago
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    it might help to simplify the first part first :)

  8. anonymous
    • one year ago
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    i got 3

  9. freckles
    • one year ago
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    after simplifying \[2(-1)^3-(-1)+(-1)^2+1?\]

  10. anonymous
    • one year ago
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    wait -2

  11. anonymous
    • one year ago
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    i used my calculator

  12. freckles
    • one year ago
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    \[-2m^3-m+m^2+1 \\ \text{ plug in } -1 \text{ since we have that we are dividing by } m-(-1) \\ -2(-1)^3-(-1)+(-1)^2+1\] \[(-1)^3=(-1)(-1)(-1)=(1)(-1)=-1 \\ \text{ and } \\ (-1)^2=(-1)(-1)=1 \\ \text{ so you really have } -2(-1)-(-1)+1+1 \\ \text{ and we also know } -2(-1)=2 \text{ and } -(-1)=+1 \\ \text{ so we have } 2+1+1+1\]

  13. freckles
    • one year ago
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    2+3 should be 5 then you need to figure out what you can add to 5 that will give you 0

  14. anonymous
    • one year ago
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    5+-5=0

  15. freckles
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    Thank you, i understand it now

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