How do you completely factor #x^3-x^2-14x+25# given x-3 is one of the factors?

1 Answer
Nov 2, 2016

Answer:

#x-3# is not a factor.

Explanation:

Factor #x^3-x^2-14x+25# given #x-3# is a factor.

Use synthetic division.

#3|1color(white)(aa)-1color(white)(aa)-14color(white)(aaa)25#
#color(white)(aa)darrcolor(white)(aaaa)3color(white)(aaaaa)6color(white)(a)-24#
#color(white)(aaa)#--------------------------------
#color(white)(aaa)1color(white)(a^22aa)2color(white)(a^2a)-8color(white)(aaa)1#

The remainder is 1 instead of zero, so #x-3# is not a factor.

Perhaps the #25# was a typo, and should have been a #24#.