Posted by Ka on Saturday, January 1, 2011 at 5:18pm.
Please help me factor this.
x(x^34x^2+3x+18) (using synthetic division please.) Thank You.

Math  Marth, Saturday, January 1, 2011 at 5:31pm
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. 
Math  Henry, Monday, January 3, 2011 at 4:51pm
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,
x2 = 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).