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

1 Answer
Jun 14, 2018

(x-2)(x-3)(x-7)

Explanation:

If the roots of the cubic are integer, then they must divide into 42. Possible candidates, plus or minus: 1, 2, 3, 6, 7, 14, 21, 42.

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