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# Find the limit of $\frac{t^3-4t+192}{t^2-t-42}$ as $t$ approaches $-6$

## Step-by-step Solution

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Solving: $\lim_{t\to-6}\left(\frac{t^3-4t+192}{t^2-t-42}\right)$

## Final Answer

$-8$
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## Step-by-step Solution

Problem to solve:

$\lim_{t\to-6}\left(\frac{t^3-4t+192}{t^2-t-42}\right)$

Choose the solving method

1

Factor the trinomial $t^2-t-42$ finding two numbers that multiply to form $-42$ and added form $-1$

$\begin{matrix}\left(6\right)\left(-7\right)=-42\\ \left(6\right)+\left(-7\right)=-1\end{matrix}$

Learn how to solve limits by factoring problems step by step online.

$\begin{matrix}\left(6\right)\left(-7\right)=-42\\ \left(6\right)+\left(-7\right)=-1\end{matrix}$

Learn how to solve limits by factoring problems step by step online. Find the limit of (t^3-4t+192)/(t^2-t-42) as t approaches -6. Factor the trinomial t^2-t-42 finding two numbers that multiply to form -42 and added form -1. Thus. We can factor the polynomial t^3-4t+192 using the rational root theorem, which guarantees that for a polynomial of the form a_nx^n+a_{n-1}x^{n-1}+\dots+a_0 there is a rational root of the form \pm\frac{p}{q}, where p belongs to the divisors of the constant term a_0, and q belongs to the divisors of the leading coefficient a_n. List all divisors p of the constant term a_0, which equals 192. Next, list all divisors of the leading coefficient a_n, which equals 1.

## Final Answer

$-8$
SnapXam A2
Answer Assistant

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Tips on how to improve your answer:

$\lim_{t\to-6}\left(\frac{t^3-4t+192}{t^2-t-42}\right)$

### Main topic:

Limits by factoring

~ 0.09 s