Posted by Ka on Saturday, January 1, 2011 at 5:18pm.
The possible rational factors are (+/-){factors of 18}/{factors of 1}: 18 is the coefficient of the x^0 term, and 1 is the coefficient of the greatest power of x - x^3 term.
= (+/-){1, 2, 3, 6, 9, 18}/{1} = (+/-){1, 2, 3, 6, 9, 18}.
Try factors using synthetic division until you find one that works. After, you will be left with a quadratic which is more easily factored.
X(-X^3 - 4X^2 + 3X + 18).
It was determined by trial and error
that when X = 2, the quantity in paren-
thesis = 0. Therefore,
x = 2,
x-2 = 0,
Using synthetic division:
(-X^3 - 4X^2 + 3X + 18) / (X - 2) =
-X^2 - 6X - 9,
Our Eq is now:
X(X - 2)(-X^2 - 6X - 9),
The trinomial = 0 when X = -3,
X = -3,
X + 3 = 0,
Using synthetic division:
(-X^2 - 6X - 9) / (X + 3) = -X - 3,
Factored Eq: X(X - 2)(X + 3)(-X - 3).