which terms could have a greatest common factor of 5m²n²? select two options. m⁵n⁵ 5m⁴n³ 10m⁴n 15m²n² 24m³n⁴

Explanation:

Step1: Analyze coefficient and exponents

For a term to have a GCF of $5m^{2}n^{2}$, the coefficient must be a multiple of 5 and the exponents of $m$ and $n$ must be at least 2.

Step2: Check option 1

For $m^{5}n^{5}$, coefficient is 1, not a multiple of 5.

Step3: Check option 2

For $5m^{4}n^{3}$, coefficient is 5, exponent of $m$ is 4 $\geq$ 2, exponent of $n$ is 3 $\geq$ 2.

Step4: Check option 3

For $10m^{4}n$, exponent of $n$ is 1 $<$ 2.

Step5: Check option 4

For $15m^{2}n^{2}$, coefficient is 15 (multiple of 5), exponent of $m$ is 2, exponent of $n$ is 2.

Step6: Check option 5

For $24m^{3}n^{4}$, coefficient is 24, not a multiple of 5.

Answer:

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