I get an error when using latex so
to factor this limit:
2x^2 - x - 3 = (2x-3)(x+1)
x^3 + 2x^2 + 6x + 5 = (x+1)(x^2+x+5)
the term (x+1) cancels out,and you can compute the limit.
Given a polynomial:
If a rational root of this polynomial exists it will be of the form:
In this case we have:
So if there is a factor of this over the rational numbers it will be of the form:
So the possible rational factors of are:
You can try each of these and find that (x + 1) is the only linear rational factor.