Algebra 1: Common Core (15th Edition)

$g(g^3+24g^2+12g+4)$
The first step in factoring $g^4+24g^3+12g^2+4g$ is to find the GCF of its terms. In order to find the GCF of a set of terms, we list the prime factors of each of the terms, figure out which prime factors are shared by all of the terms, and then multiply the shared factors: The prime factors of $g^4$ are $g×g×g×g$ The prime factors of $24g^3$ are $2\times 2×2×3×g×g×g$ The prime factors of $12g^2$ are $2\times2\times 3\times g×g$ The prime factors of $4g$ are $2\times2\times g$ The only common prime factor is $g$, so $g$ is the GCF of the terms. We take this GCF out, and multiply the GCF by the original expression divided by the GCF (to divide, we simply cancel out all of the common prime factors), giving us the factored form of the expression: $g(g^3+24g^2+12g+4)$