Find all values of c such that the limit exists

Question

lim
x-->1 (x^2 + 3x + c) / (x-1)

Answer 1

for the limit to exist, x-1 has to divide evenly into
x^2 + 3x + c

let f(x) = x^2 + 3x + c
f(1) = 0 = 1 + 3 + c
c = -4

check:
lim (x^2 + 3x - 4)/(x-1) as x -->1
= lim (x+4)(x-1)/(x-1) as x ---> 1
= lim x+4
= 5 , the limit exists when c = -4