Question

If (3x^4-5x^2+x-2) / (x+1) has the same remainder as (4x^3+2x^5-k) / (x-1). Find k. Full solutions or instructions would be helpful.

Answer 1

replace \(x\) by \(-1\) in
\[3x^4-5x^2+x-2\] to find the remainder
then replace \(x\) by \(1\) in the second expression, set it equal to the answer you got from the first part, and solve for \(k\)

Answer 2

if it is not clear, or not clear why this works, let me know

Answer 3

k is 11 but im getting 5 = 6-k for my last row

Answer 4

its using remainder theorem btw

Answer 5

yes, what did you get for the remainder for the first part?

Answer 6

i see the problem
the remainder is \(-5\) not \(5\)

Answer 7

if you are using synthetic division that if fine, but the numbers -1and 1 are easy to use, so you can evaluate the numerator at -1 to get the remainder for the first one
it is \(-5\)

Answer 8

if you replace \(x\) by 1 in the second you get \(6-k\) so set \(-5=6-k\) and you will get your 11

Answer 9

i'll reevaluate it. i may have done my adding wrong. thanks!

Answer 10

yw
but at the risk of repeating myself, it is easy to replace \(x\) by \(-1\) rather than doing the synthetic division

Answer 11

i got it, i multiplied the negatives wrong. thanks again

Answer 12

you can pretty much do it in your head

Answer 13

yw (again)