Question

factor out the greatest common factor from the polynomial.
-6p^4q^2 - 2p^3q^3
-6p^4q^2 - 2p^3q^3 =

Explanation:

Step1: Identify GCF of coefficients

The coefficients are -6 and -2. The GCF of 6 and 2 is 2, and considering the negative - signs, the GCF of -6 and -2 is -2.

Step2: Identify GCF of variables

For the $p$ - terms $p^{4}$ and $p^{3}$, the GCF is $p^{3}$ (using the rule that for $a^{m}$ and $a^{n}$ with $m>n$, the GCF is $a^{n}$). For the $q$ - terms $q^{2}$ and $q^{3}$, the GCF is $q^{2}$.

Step3: Factor out the GCF

Factor out $- 2p^{3}q^{2}$ from the polynomial $-6p^{4}q^{2}-2p^{3}q^{3}$. We get $-2p^{3}q^{2}(3p + q)$.

Answer:

$-2p^{3}q^{2}(3p + q)$