# Limit. lim_(xirghtarrow 2)(3x^2 -5x-2)/(x-2)

Limit. $\underset{x\to 2}{lim}﻿\frac{3{x}^{2}-5x-2}{x-2}$
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cindysnifflesuz
I'm assuming (x-2) is all in the denominator:
$\underset{x\to 2}{lim}\frac{3{x}^{2}-5x-2}{x-2}$
Factor numerator:
$\underset{x\to 2}{lim}\frac{\left(x-2\right)\left(3x+1\right)}{x-2}$
$\underset{x\to 2}{lim}\left(3x+1\right)=3\left(2\right)+1=6$
ETA: factoring steps
$a{x}^{2}+bx+c$
You want two numbers that give you (a*c) and add up to b.
ac = -6
b = -5
The two numbers you want are -6 and 1.
Rewrite term "bx":
$3{x}^{2}-6x+x-2$
Factor by grouping:
$\left(3{x}^{2}-6x\right)\left(+x-2\right)$
3x(x-2)+1(x-2) [two inner parentheses should be the same]
(3x+1)(x-2)