Question

remove the largest possible common factor. check your answer by multiplication.
$9x^4 - 6x^3 - 12x$
factor out the greatest common factor
$9x^4 - 6x^3 - 12x = \square$

Explanation:

Step1: Find GCF of coefficients

The coefficients are 9, -6, -12. The greatest common factor of 9, 6, 12 is 3.

Step2: Find GCF of variable terms

The variable terms are $x^4$, $x^3$, $x$. The greatest common factor is $x$.

Step3: Factor out overall GCF

Factor $3x$ from each term of the polynomial:
$9x^4 - 6x^3 - 12x = 3x(3x^3 - 2x^2 - 4)$

Step4: Verify via multiplication

Multiply $3x$ with the factored polynomial:
$3x \cdot 3x^3 + 3x \cdot (-2x^2) + 3x \cdot (-4) = 9x^4 - 6x^3 - 12x$, which matches the original expression.

Answer:

$3x(3x^3 - 2x^2 - 4)$