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Factor the trinomial $x^2-5x+6$ finding two numbers that multiply to form $6$ and added form $-5$
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$\begin{matrix}\left(-2\right)\left(-3\right)=6\\ \left(-2\right)+\left(-3\right)=-5\end{matrix}$
Learn how to solve limits by direct substitution problems step by step online. Find the limit (x)->(2)lim((x^2-5x+6)/(3x^3-5x^2-x+-2)). Factor the trinomial x^2-5x+6 finding two numbers that multiply to form 6 and added form -5. Thus. We can factor the polynomial 3x^3-5x^2-x-2 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 -2. Next, list all divisors of the leading coefficient a_n, which equals 3.