Step-by-step Solution

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

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Step-by-step explanation

Problem to solve:

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

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

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

Unlock this full step-by-step solution!

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.

Final Answer

$t+1+\frac{39}{t-7}$

Problem Analysis

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

Main topic:

Limits by factoring

Time to solve it:

~ 0.1 seconds