# Limit of a rational with polynomials

• Dec 31st 2009, 11:45 AM
nautica17
Limit of a rational with polynomials
I'm stuck on this practice problem.. and it's the algebra that is getting to me. Take a look:

lim x-> 2 of ( (x^3 + 3x^2 - 12x + 4) / (x^3 - 4x) )

I've figured that I factor out the top and bottom and I've done so with the denominator and got x(x-2)(x+2), but the numerator is what I am stuck on. Can anyone push me in the right direction? I'm getting this as my numerator: (x^2 - 4)(x+3)(3x+1) ... and that obviously makes no sense what so ever.

• Dec 31st 2009, 12:04 PM
Plato
Quote:

Originally Posted by nautica17
lim x-> 2 of ( (x^3 + 3x^2 - 12x + 4) / (x^3 - 4x) )

$x^3+3x^2-12x+4=(x-2)(x^2+5x-2)$
• Dec 31st 2009, 12:16 PM
nautica17
Quote:

Originally Posted by Plato
$x^3+3x^2-12x+4=(x-2)(x^2+5x-2)$

Hmm.. well that works. Thank-you. If it's not too much trouble could you show me how to do that? I cannot figure out how to pull the (x-2) out.
• Dec 31st 2009, 12:24 PM
Plato
Quote:

Originally Posted by nautica17
Hmm.. well that works. Thank-you. If it's not too much trouble could you show me how to do that? I cannot figure out how to pull the (x-2) out.

Because $x=2$ is a root of the numerator then $(x-2)$ must be a factor.
So use simple long division.