# How do you factor x^3-12x^2+41x-42?

Jun 14, 2018

$\left(x - 2\right) \left(x - 3\right) \left(x - 7\right)$
A little exploration with a calculator reveals that both $x = 2$ and $x = 3$ are roots, so we can immediately factor the expression as
$\left(x - 2\right) \left(x - 3\right) \left(x - 7\right)$, deducing from $42 = 2 \cdot 3 \cdot 7$ that the third root must be 7.