Expert: Richard J. Raridon - 9/11/2006

Question
Can this be factored? Because I can't factor it. Its from my textbook. My textbook wants me to solve for x by factoring.

x^3 + 20x^2 + 133x + 294 = 0

Thank You for helping me.

Answer
re-write it as f(x) = x^3+20x^2+133x+294.
if x=a is a solution then f(a) = 0.
in this case, obviously, a has to be negative.  
f(0) = 294 and f(-10) = -36 so you know that a solution exists between 0 and -10.  
trial and error will lead you to x=-7 as a solution, so one of the factors is (x+7).
Simply divide that into the original expression to get
x^2+13x+42 which you can easily factor into (x+6)(x+7)