## Step-by-step explanation

Problem to solve:

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. Evaluate the limit of (t^3-4t+192)/(t^2-t-42) as x 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.