Polynomial Functions Question

[malkuthe]

I normally don't have that many problems with math but this one problem has had me stuck for the past three days.

If the remainder of a polynomial function P(x) when it is divided by (x-2) is k+10, and P(1)=4, what is the value of k?

It would be really appreciated if you could help me out. I've racked my brain for the answer but I still can't find any way of applying the division algorithm or the remainder theorem to find an answer.

[malkuthe]

For anyone who might be interested in the answer to this one, I'm pretty sure it's all values of k such that k is an element of the set of real numbers.

My class won't be checking it until after spring break, but I wrote up a proof for my answer, which you can look at here: https://docs.google.com/document/d/1nXF3BdmfWsECnx20QylykYUdAZWtz7So8OvVHSs2a88/edit?usp=sharing

[stapel_eliz]

There could be quibbles with your statements to "let n = 2n" and "let n = 2n - 1". It might be better to say "let n = 2m" and "let n = 2m - 1".

But your general proof that "the" value of k is actually any real number could explain why I've been spinning my wheels all weekend trying, without success, to figure out a way to isolate one numerical value.

[malkuthe]

Yeah, I realized that when I was writing it down for the proof I was submitting to my teacher. But I corrected it there and I realize I should be correcting it on the document.

And yeah, I spent quite a few days trying without success either, so, at least now we know there isn't a discrete answer!