Question

select all the correct answers.
select the expressions that all have the following quotient.
$2m + 3$
$\square$ $(4m^{2} + 6m) \div 2m$
$\square$ $(10m^{2} + 15m) \div 5m$
$\square$ $(32m + 48m^{2}) \div 16m$
$\square$ $(10m + 15m^{2}) \div 5m$
$\square$ $(32m^{2} + 48m) \div 16m$
$\square$ $(4m + 12) \div 2m$

Explanation:

Step1: Simplify \((4m^{2}+6m)\div2m\)

Divide each term in the numerator by \(2m\): \(\frac{4m^{2}}{2m}+\frac{6m}{2m}=2m + 3\)

Step2: Simplify \((10m^{2}+15m)\div5m\)

Divide each term in the numerator by \(5m\): \(\frac{10m^{2}}{5m}+\frac{15m}{5m}=2m + 3\)

Step3: Simplify \((32m + 48m^{2})\div16m\)

Divide each term in the numerator by \(16m\): \(\frac{32m}{16m}+\frac{48m^{2}}{16m}=2 + 3m\) (not equal to \(2m+3\))

Step4: Simplify \((10m + 15m^{2})\div5m\)

Divide each term in the numerator by \(5m\): \(\frac{10m}{5m}+\frac{15m^{2}}{5m}=2 + 3m\) (not equal to \(2m+3\))

Step5: Simplify \((32m^{2}+48m)\div16m\)

Divide each term in the numerator by \(16m\): \(\frac{32m^{2}}{16m}+\frac{48m}{16m}=2m + 3\)

Step6: Simplify \((4m + 12)\div2m\)

Divide each term in the numerator by \(2m\): \(\frac{4m}{2m}+\frac{12}{2m}=2+\frac{6}{m}\) (not equal to \(2m+3\))

Answer:

The correct expressions are:
\((4m^{2}+6m)\div2m\)
\((10m^{2}+15m)\div5m\)
\((32m^{2}+48m)\div16m\)