1. ## Limits

Hi how can i factor this limit?

Find the limit
$\displaystyle \lim_{x \to -1} \frac{2x^2 - x - 3}{x^3+2x^2+6x+5}$

2. 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.

3. THanks you very much parallel

how did you factor the denominator?

THanks you very much parallel

how did you factor the denominator?
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