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burhan101

  • 3 years ago

When polynomial mx³-3x²+nx+2 is divided by x+3, the remainder is -1. When it is divided by x-2, the remainder is -4. Determine the values of 'm' and 'n'.

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  1. helder_edwin
    • 3 years ago
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    use synthetic division

  2. lgbasallote
    • 3 years ago
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    are you familiar with the remainder theorem?

  3. helder_edwin
    • 3 years ago
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    that's better. sorry

  4. burhan101
    • 3 years ago
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    |dw:1347327495204:dw|

  5. burhan101
    • 3 years ago
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    and yes i am familiar with the remainder theorem, am i doing this right so far ?

  6. lgbasallote
    • 3 years ago
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    yup

  7. lgbasallote
    • 3 years ago
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    now...just add 1 to both sides...to get something fun

  8. burhan101
    • 3 years ago
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    |dw:1347327616779:dw|

  9. lgbasallote
    • 3 years ago
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    right to..add 4 to both sides there

  10. lgbasallote
    • 3 years ago
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    too*

  11. burhan101
    • 3 years ago
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    |dw:1347327802473:dw|

  12. burhan101
    • 3 years ago
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    now i dont know what to do next

  13. lgbasallote
    • 3 years ago
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    yes. now simplify those

  14. lgbasallote
    • 3 years ago
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    -27m -3n - 24 = 0 everything is divisible by 3

  15. lgbasallote
    • 3 years ago
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    8m + 2n - 6 = 0 everything is divisible by 2

  16. burhan101
    • 3 years ago
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    |dw:1347327965579:dw|

  17. burhan101
    • 3 years ago
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    like that ?

  18. burhan101
    • 3 years ago
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    or with the coeff

  19. lgbasallote
    • 3 years ago
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    right

  20. lgbasallote
    • 3 years ago
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    -9m - n - 8 = 0 4m + n - 3 = 0 now you can do system of linear eqn

  21. burhan101
    • 3 years ago
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    i can let is equal any number right ?

  22. lgbasallote
    • 3 years ago
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    yes. you can also do elimination

  23. burhan101
    • 3 years ago
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    let m=1 -9(1)-n-8=0 -9-n-8=0 -n=9+8 n=17 subst. n=17 in 2nd equation 4m+17-3=0 4m+14=0 m= -7/2

  24. lgbasallote
    • 3 years ago
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    that's an unorthodox method...

  25. lgbasallote
    • 3 years ago
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    where did you learn that?

  26. burhan101
    • 3 years ago
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    i dont know, i think im confusing it with something else

  27. lgbasallote
    • 3 years ago
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    it's the plotting of points method...it doesn't work here lol

  28. burhan101
    • 3 years ago
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    oh woops !

  29. lgbasallote
    • 3 years ago
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    anyway... -9m - n - 8 = 0 4m + n - 3 = 0 try adding the equations...what do you get?

  30. burhan101
    • 3 years ago
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    m= -11/5

  31. burhan101
    • 3 years ago
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    and now subst

  32. lgbasallote
    • 3 years ago
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    right

  33. burhan101
    • 3 years ago
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    n=29/5

  34. lgbasallote
    • 3 years ago
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    right. so there you go

  35. burhan101
    • 3 years ago
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    thank you so much ! :)

  36. lgbasallote
    • 3 years ago
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    welcome

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