I hope someone can provide me with some clarification.
I'm trying to find the remainder for a dividend of x^2+9x-7. I already have information regarding the quotient and divisor: (x + 3) and (x + 5). It's unknown which one is the quotient or divisor, but I don't think that's relevant information anyways. One method of solving the remainder would be to isolate the remainder ("r") in the given equation: (x + 3)(x + 5) + r = x^2 + 9x - 7. This works for me, and I get the correct answer of r = x - 22.
However, I don't understand why I ALSO can't use the remainder theorem to solve this. While I understand that a solution with a variable is impossible to solve with the remainder theorem, how would I know this prior to using the theorem? I thought that when factors have a degree of 1, that you could find the remainder by simply using the remainder theorem - clearly this case is different. Please help!!!!