which terms could have a greatest common factor of $5m^{2}n^{2}$? select two options.\n$m^{5}n^{5}$\n$5m^{4}n…

Explanation:

Step1: Analyze the GCF components

The GCF is $5m^{2}n^{2}$. We need terms that have 5 as a factor of the coefficient and $m^{2}$ and $n^{2}$ as factors of the variables.

Step2: Check each option

• For $m^{5}n^{5}$, the coefficient is 1, not divisible by 5, so it's not a candidate.
• For $5m^{4}n^{3}$, the coefficient is 5, and $m^{2}$ and $n^{2}$ are factors of $m^{4}n^{3}$ since $m^{4}n^{3}=m^{2}\times m^{2}\times n^{2}\times n$.
• For $10m^{4}n$, the coefficient is divisible by 5, but $n^{2}$ is not a factor of $n$, so it's not a candidate.
• For $15m^{2}n^{2}$, the coefficient is divisible by 5, and $m^{2}n^{2}$ is the same as in the GCF.
• For $24m^{3}n^{4}$, the coefficient is not divisible by 5, so it's not a candidate.

Answer:

B. $5m^{4}n^{3}$, D. $15m^{2}n^{2}$