which term can be added to the list so that the greatest common factor of the three terms is 12h³? 36h³…

Explanation:

Step1: Analyze factors of given terms

The factors of $36h^{3}=2\times2\times3\times3\times h\times h\times h$ and $12h^{6}=2\times2\times3\times h\times h\times h\times h\times h\times h$. The GCF we want is $12h^{3}=2\times2\times3\times h\times h\times h$.

Step2: Analyze each option

• For $6h^{3}=2\times3\times h\times h\times h$, the GCF of $36h^{3}, 12h^{6},6h^{3}$ is $6h^{3}$, not $12h^{3}$.
• For $12h^{2}=2\times2\times3\times h\times h$, the GCF of $36h^{3}, 12h^{6},12h^{2}$ is $12h^{2}$, not $12h^{3}$.
• For $30h^{4}=2\times3\times5\times h\times h\times h\times h$, the GCF of $36h^{3}, 12h^{6},30h^{4}$ is $6h^{3}$, not $12h^{3}$.
• For $48h^{5}=2\times2\times2\times2\times3\times h\times h\times h\times h\times h$, the GCF of $36h^{3}, 12h^{6},48h^{5}$ is $12h^{3}$.

Answer:

$48h^{5}$