Question

1. $6f^{5}g^{3} + 12f^{2}g - 30f^{3}g^{3}$

Explanation:

Step1: Identify greatest common factor

The GCF of coefficients 6, 12, 30 is 6. The GCF of $f^5, f^2, f^3$ is $f^2$. The GCF of $g^3, g, g^3$ is $g$. Overall GCF: $6f^2g$

Step2: Factor out GCF from each term

$\frac{6f^5g^3}{6f^2g} + \frac{12f^2g}{6f^2g} - \frac{30f^3g^3}{6f^2g}$
Simplify each term: $f^3g^2 + 2 - 5fg^2$

Step3: Write factored expression

Combine GCF and simplified terms

Answer:

$6f^2g(f^3g^2 - 5fg^2 + 2)$