when x^2 - 2x - 1 is divided by P(x), the quotient is x+2 and the remainder is 7, then what is P(x)?

Question

Thank you very much for your answer. :>

Answer 1

divide x+b into x^2-2x -1

to get

x-2b + remainder of b^2+2b-1=7

b^2 +2b -8 = 0

(b+4)(b-2) = 0

b = -4 or 2

P(x) = x-2b = x+8 or x-4

P(x) = x-4 is the answer. Ignore x+8

divide x+2 into x^2 -2x -1

to get

x-4 + remainder = 7

(x+2)(x-4) = x^2 -2x -8 = x^2-2x -1 -7

P(x) = x-4

divide x-4 into x^2 -2x -1

to get x+2 with a remainder of 7