Find the remainder when f(x) = −2x3 + 24x2 − 58x + 40 is divided by x − 9.
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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.
the remainder theorem says we can just evaluate f(9)
Exactly! I inputted that value, but I came up with an incorrect answer. Did I make an arithmetic error?
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I don't know
I came up with -396 when evaluating the function for the value of 9.
@freckles is there anyway you could evaluate the function, for f(9), and see what you come up with?
Thanks for your previous help with the concepts of the Theorems as well, it really helped!
\[f(9)=-2(9)^3+24(9)^2-58(9)+40 \\ f(9)=-2(729)+24(81)-58(9)+40 \\ f(9)=-1458+1944-522+50 \\ f(9)=486-522+50 \\ f(9)=-522+486+50 \\ f(9)=-522+536 \\ f(9)=536-522=14\]
is this what you did ?
I did it without a calculator
so you might want to check
oops I put 50 instead of 40
just take away 10
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.
By subtracting 10 from the final output, your answer is correct. Thanks again for all your help!
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