Question

Which terms could have a greatest common factor of $5m^2{n}^2$ check all that apply.

• A. $m^5{n}^5$
• B. $5m^4{n}^3$
• C. $10m^{4}n$
• D. $15m^2{n}^2$
• E. $24m^3{n}^4$

Answer 1

Answer: (B), (D)

$15m^2{n}^2$

Step 1: Explanation for correct option:

Factor the monomial $5m^4{n}^3$.

$5m^4{n}^3=5m^2{n}^2\left(m^{2}n\right)$

The greatest common factor is $5m^2{n}^2$.

So option $\left(B\right)$ is correct.

Factor the monomial $15m^2{n}^2$.

$15m^2{n}^2=5m^2{n}^2\left(3\right)$.

The greatest common factor is $5m^2{n}^2$.

So option $\left(D\right)$ is correct.

Step 2: Explanation for incorrect option.

Factor the monomial $m^5{n}^5$.

$m^5{n}^5=1\left(m^5{n}^5\right)$

The greatest common factor is not a $5m^2{n}^2$.

So option $\left(A\right)$ is not correct.

Factor the monomial $10m^{4}n$.

$10m^{4}n=10m^{2}n\left(m^2\right)$

The greatest common factor is not a $5m^2{n}^2$.

So option $\left(C\right)$ is not correct.

Factor the monomial $24m^3{n}^4$.

$24m^3{n}^4=24m^2{n}^2\left(m{n}^2\right)$

The greatest common factor is not a $5m^2{n}^2$.

So option $\left(E\right)$ is not correct.

Hence, the correct options are $\left(B\right)and\left(D\right).$