is K negative or positive?

[relentlesspursuito700plus]

So while working through a problem, I found out that (r-8) is a factor of (r^2) - kr - 56, and needed to find out what k was. Simple, right?
(r-8)(r+7) and that gives the answer right? Here is where I am confused. Is the integer k negative or positive? I don't it sounds like a dumb question, but I've gotten a similar problem incorrect because of that issue. When you simplify (r-8)(r+7)= (r^2)+7r-8r+56. So then that becomes (r^2)-1r-56. Since negative 8 plus positive 7 equals negative 1, shouldn't k be negative 1? The answer given was 1, but -1 was one of the choices, which is what I picked. Can someone explain this very basic concept to me? I feel stupid for even asking this question. Email to: alternative email account 00 (at) gmail would be greatly appreciated. Thanks!

[relentlesspursuito700plus]

Again.. didn't I know I had to source it. Sorry.

[RonPurewal]

So while working through a problem, I found out that (r-8) is a factor of (r^2) - kr - 56, and needed to find out what k was. Simple, right?
(r-8)(r+7) and that gives the answer right? Here is where I am confused. Is the integer k negative or positive? I don't it sounds like a dumb question, but I've gotten a similar problem incorrect because of that issue. When you simplify (r-8)(r+7)= (r^2)+7r-8r+56. So then that becomes (r^2)-1r-56. Since negative 8 plus positive 7 equals negative 1, shouldn't k be negative 1? The answer given was 1, but -1 was one of the choices, which is what I picked. Can someone explain this very basic concept to me? I feel stupid for even asking this question. Email to: alternative email account 00 (at) gmail would be greatly appreciated. Thanks!

not a stupid question. in fact, BINARY choices (choices with exactly two options, like this one) tend to be the easiest things of all to confuse!

you just have to notice the TOTAL PARALLELISM of the two expressions. notice the orange colored parts below:

r^2 - kr - 56 = r^2 - 1r - 56
reading only the orange parts, you can see that NEGATIVE "k" equals NEGATIVE one.
therefore, k = 1.

it all boils down to: watch the signs!
watch them on BOTH sides of the equation!

make sense?