Question

Please help me factor this.
x(-x^3-4x^2+3x+18) (using synthetic division please.) Thank You.

Answer 1

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.

Answer 2

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).