Question
Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.
15g9+15g6+15g3–15
Questions
15g9+15g6+15g3–15
Questions
Answers
GPT-4o mini
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:
1. The GCF of \( 15g^9, 15g^6, 15g^3, \) and \( -15 \) is \( 15 \).
2. 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:
\[
15(g^6 + g^3 + 1)
\]
The coefficients are all multiples of 15, and the terms involving \( g \) can be factored out as follows:
1. The GCF of \( 15g^9, 15g^6, 15g^3, \) and \( -15 \) is \( 15 \).
2. 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:
\[
15(g^6 + g^3 + 1)
\]