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anonymous

  • one year ago

Find the remainder when f(x) = −2x3 + 24x2 − 58x + 40 is divided by x − 9.

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  1. anonymous
    • one year ago
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    I attempted to do this problem using the Remainder Theorem and came up with an incorrect answer. Please show work so I can better understand why I got the problem wrong.

  2. freckles
    • one year ago
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    the remainder theorem says we can just evaluate f(9)

  3. anonymous
    • one year ago
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    Exactly! I inputted that value, but I came up with an incorrect answer. Did I make an arithmetic error?

  4. freckles
    • one year ago
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    perhaps I don't know

  5. anonymous
    • one year ago
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    I came up with -396 when evaluating the function for the value of 9.

  6. anonymous
    • one year ago
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    @freckles is there anyway you could evaluate the function, for f(9), and see what you come up with?

  7. anonymous
    • one year ago
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    Thanks for your previous help with the concepts of the Theorems as well, it really helped!

  8. freckles
    • one year ago
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    \[f(9)=-2(9)^3+24(9)^2-58(9)+40 \\ f(9)=-2(729)+24(81)-58(9)+40 \\ f(9)=-1458+1944-522+50 \\ f(9)=486-522+50 \\ f(9)=-522+486+50 \\ f(9)=-522+536 \\ f(9)=536-522=14\] is this what you did ? I did it without a calculator so you might want to check

  9. freckles
    • one year ago
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    oops I put 50 instead of 40

  10. freckles
    • one year ago
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    just take away 10

  11. anonymous
    • one year ago
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    I see my egregious error quite clearly now. For some reason my calculator came up with 261 instead of 729 for 9^3, I must've inputted it incorrectly.

  12. anonymous
    • one year ago
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    By subtracting 10 from the final output, your answer is correct. Thanks again for all your help!

  13. freckles
    • one year ago
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    yeah I accidentally put 50 on that 3rd line and kept it as 50 that is why my answer was 10 units more than what it should have been

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