Question

find the greatest monomial that is a factor of the expression:
$12f^4g^2 + 15fg^2 - 3f^3g^3$
$\circ\\ 3fg^2$
$\circ\\ 3g^2$
$\circ\\ 6fg^2$
$\circ\\ 6f^4g^2$

Explanation:

Step1: Find GCF of coefficients

The coefficients are 12, 15, -3. The GCF of 12, 15, 3 is 3.

Step2: Find GCF of \( f \) terms

For \( f \): exponents are 4, 1, 3. The smallest exponent is 1, so \( f^1 = f \).

Step3: Find GCF of \( g \) terms

For \( g \): exponents are 2, 2, 3. The smallest exponent is 2, so \( g^2 \).

Step4: Combine GCFs

Multiply the GCF of coefficients, \( f \), and \( g \): \( 3 \times f \times g^2 = 3fg^2 \).

Answer:

A. \( 3fg^2 \)