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Factor out the greatest common factor. If the greatest common factor is $1$ , just retype the polynomial. $\newline$ $8g^3 - 6g^2$

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Factor out a monomial

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Q. Factor out the greatest common factor. If the greatest common factor is

1

, just retype the polynomial.

\newline

8g^3 - 6g^2

Find GCF of Terms: We need to find the greatest common factor (GCF) of the terms $8g^3$ and $6g^2$ . To do this, we will list the prime factors of the coefficients and the common powers of $g$ . $\newline$ $8g^3 = 2 \times 2 \times 2 \times g \times g \times g$ $\newline$ $6g^2 = 2 \times 3 \times g \times g$ $\newline$ The common factors are $2$ , $g$ , and $g$ . $\newline$ $2 \times g \times g = 2g^2$ $\newline$ So, the GCF of $8g^3$ and $6g^2$ is $6g^2$ $1$ .
Express Terms as Product: Now we will express each term as the product of the GCF and the remaining factors. $\newline$ For $8g^3$ , we have: $\newline$ $8g^3 = 2 \times 2 \times 2 \times g \times g \times g$ $\newline$ $8g^3 = 2g^2 \times 4g$ $\newline$ For $6g^2$ , we have: $\newline$ $6g^2 = 2 \times 3 \times g \times g$ $\newline$ $6g^2 = 2g^2 \times 3$
Factor Out GCF from Polynomial: We can now factor out the GCF from the polynomial $8g^3 - 6g^2$ .
$8g^3 - 6g^2$
$= 2g^2 * 4g - 2g^2 * 3$
$= 2g^2(4g - 3)$
This is the factored form of the polynomial.

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