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

1 Answer
Jun 14, 2018

Answer:

#(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.