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Factor the trinomial $t^2-t-42$ finding two numbers that multiply to form $-42$ and added form $-1$
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$\begin{matrix}\left(6\right)\left(-7\right)=-42\\ \left(6\right)+\left(-7\right)=-1\end{matrix}$
Learn how to solve limits by direct substitution problems step by step online. Find the limit (t)->(-6)lim((t^3-4t+192)/(t^2-t+-42)). 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.