Question

factor out the greatest common factor.
$-6x^{5} + 12x^{4} + 18x^{3}$
$?x^{\square}(-x^{\square} + 2x + 3)$

Explanation:

Step1: Identify GCF of coefficients

The coefficients are $-6$, $12$, $18$. The greatest common factor of their absolute values $6$, $12$, $18$ is $6$.

Step2: Identify GCF of variables

The variable terms are $x^5$, $x^4$, $x^3$. The greatest common factor is $x^3$.

Step3: Factor out overall GCF

Factor $6x^3$ from each term:
$$-6x^5 + 12x^4 + 18x^3 = 6x^3(-x^2 + 2x + 3)$$

Answer:

The filled expression is $\boldsymbol{6x^3(-x^2 + 2x + 3)}$, so the missing values are 6, 3, and 2 respectively.