Hi how can i factor this limit?
Find the limit
$\displaystyle \lim_{x \to -1} \frac{2x^2 - x - 3}{x^3+2x^2+6x+5}$
Do you know the Rational Roots Theorem?
Given a polynomial:
$\displaystyle px^n + ax^{n-1} + ... + bx + q = 0$
If a rational root of this polynomial exists it will be of the form:
$\displaystyle x = \frac{\text{factor of q}}{\text{factor of p}}$
In this case we have:
$\displaystyle x^3 + 2x^2 + 6x + 5$
So if there is a factor of this over the rational numbers it will be of the form:
$\displaystyle (\text{factor of 1}) x - (\text{factor of 5})$
So the possible rational factors of $\displaystyle x^3 + 2x^2 + 6x + 5$ are:
$\displaystyle (x \pm 1)$
$\displaystyle (x \pm 5)$
You can try each of these and find that (x + 1) is the only linear rational factor.
-Dan