To factor out the greatest common factor (GCF) from the polynomial \( 5g^3 - 8g^2 \), we first identify the GCF of the terms in the expression.
The coefficients of the terms are 5 and -8, and the GCF of 5 and 8 is 1. However, we also need to consider the variable part. The terms contain \( g^3 \) and \( g^2 \), and the GCF of \( g^3 \) and \( g^2 \) is \( g^2 \).
Thus, the overall GCF of the polynomial \( 5g^3 - 8g^2 \) is \( g^2 \).
Now we factor \( g^2 \) out of each term:
\[ 5g^3 - 8g^2 = g^2(5g - 8) \]
So the factored form of the polynomial is:
\[ g^2(5g - 8) \]
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