Question

Find the constant c so that lim x->8 x^2+2x+c/x^2-15x+56 exists. For that value of c, determine the limit. (Hint: Find the value of c for which x-8 is a factor of the numerator).

I understand that I should set (x-8)(x+b) equal to x^2+2x+c but all the variables are getting confusing.

Answer 1

(x-8)(x+b) = x^2 + 2 x + c

- 8 b = c
and
-8 x + b x = 2 x
or
b = 10

so
c = -80