Question

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

Answer 1

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.

Answer 2

the remainder theorem says we can just evaluate f(9)

Answer 3

Exactly! I inputted that value, but I came up with an incorrect answer. Did I make an arithmetic error?

Answer 4

perhaps
I don't know

Answer 5

I came up with -396 when evaluating the function for the value of 9.

Answer 6

@freckles is there anyway you could evaluate the function, for f(9), and see what you come up with?

Answer 7

Thanks for your previous help with the concepts of the Theorems as well, it really helped!

Answer 8

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

Answer 9

oops I put 50 instead of 40

Answer 10

just take away 10

Answer 11

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.

Answer 12

By subtracting 10 from the final output, your answer is correct. Thanks again for all your help!

Answer 13

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