To factor out the greatest common factor (GCF) from the polynomial \( 15g^9 + 15g^6 + 15g^3 - 15 \), we first identify the GCF of the terms.
The coefficients are all multiples of 15, and the terms involving \( g \) can be factored out as follows:
- The GCF of \( 15g^9, 15g^6, 15g^3, \) and \( -15 \) is \( 15 \).
- Since \( g^3 \) is the lowest power of \( g \) in the terms containing \( g \), we will factor out \( 15g^3 \).
Now we can factor it out:
\[ 15g^9 + 15g^6 + 15g^3 - 15 = 15(g^6 + g^3 + 1 - 1/g^3) \]
Thus, factoring out \( 15 \) from the polynomial gives:
\[ 15(g^6 + g^3 + 1 - 1/g^3) \]
However, it's typical to keep the remaining factor as simplified as possible without introducing negative or fractional exponents in the context of polynomials. In simpler terms, we can rewrite:
\[ 15(g^6 + g^3 + 1 - 1) = 15(g^6 + g^3 + 1) \]
So, the final factored expression is:
\[ 15(g^6 + g^3 + 1) \]
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