Please help me factor this.
x(-x^3-4x^2+3x+18) (using synthetic division please.) Thank You.
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).
To factor this expression using synthetic division, we first need to find a root of the cubic polynomial. In this case, since we have the term "x" in front, we know that x = 0 is a root.
Using synthetic division, we'll divide the cubic polynomial, -x^3 - 4x^2 + 3x + 18, by x = 0:
0 | -1 -4 3 18
| 0 0 0
---------------------
| -1 -4 3 18
The result of this division is -1x^2 - 4x + 3, with a remainder of 18.
Now we have factored the given expression as:
x(-x^3 - 4x^2 + 3x + 18) = x(x + 0)(-1x^2 - 4x + 3)
The factorization is:
x(x)(-1x^2 - 4x + 3),
which simplifies to:
x^2(-1x^2 - 4x + 3).
Thus, using synthetic division, we factored the expression as x^2(-1x^2 - 4x + 3).