Question

1. -18xy²z² - 36xy²z - 12xy⁴z

Explanation:

Step1: Find GCF of coefficients

The coefficients are -18, -36, -12. Their greatest common factor (GCF) is -6.

Step2: Find GCF of variable terms

For $x$: each term has $x^1$, so GCF is $x$.
For $y$: terms have $y^2, y^2, y^4$, so GCF is $y^2$.
For $z$: terms have $z^2, z^1, z^1$, so GCF is $z$.
Combined variable GCF: $xy^2z$

Step3: Factor out overall GCF

Divide each term by $-6xy^2z$ and write as a product.

$$\begin{align*} -18xy^2z^2 - 36xy^2z - 12xy^4z &= -6xy^2z(3z) + (-6xy^2z)(6) + (-6xy^2z)(2y^2) \\ &= -6xy^2z(3z + 6 + 2y^2) \end{align*}$$

Answer:

$-6xy^2z(2y^2 + 3z + 6)$