# Finding limit

## Homework Statement

Find the limit of

$\frac{x^3-2x^2-9}{x^2-2x-3}$

as x->3

## The Attempt at a Solution

You factor the bottom portion and top portion, then it looks something like this

$\frac{x(x^2-2x)-9}{(x-3)(x+1)}$

I feel like I can go further about eliminating the demonimator but I dont know what

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dextercioby
Homework Helper
Is 3 a root of the polynomial x^3- 2x^2 - 9 ? If so, what is then factoring of this polynomial ?

Mark44
Mentor
(x - 3) is a factor of the numerator. You can use either synthetic division or plain old polynomial division to find the other factor.

SammyS
Staff Emeritus
Homework Helper
Gold Member
... or notice that

$x^3-2x^2-9 = x^3-3x^2+x^2-9$

and factor by grouping.

HallsofIvy
Homework Helper

## Homework Statement

Find the limit of

$\frac{x^3-2x^2-9}{x^2-2x-3}$

as x->3

## The Attempt at a Solution

You factor the bottom portion and top portion, then it looks something like this

$\frac{x(x^2-2x)-9}{(x-3)(x+1)}$
No, you did NOT factor the numerator. That is not what "factor" means.

I assume you tried first just putting x= 3 into the fraction and found that both numerator and denominator were 0 when x= 3. The fact that the numerator was 0 tells you that it has a factor of x- 3. $x^3- 2x^2- 9= (x- 3)(ax^2+ bx+ c)$
It shouldn't be hard to see what a, b, and c must be.

I feel like I can go further about eliminating the demonimator but I dont know what