Answer:
The correct option is B
Step-by-step explanation:
Now, we have to find the factors , we can use the middle terms split method, or the addition/ subtraction of the terms can be done, or we can use the division method to get the factors of the polynomials.
So here we will use the division method to find the factors, as follows:
[tex]4m^4+36m^3+96m^2+80m\\=4m\left(m^3+9m^2+24m+20\right)\\=4m \left(m+2\right)\frac{m^3+9m^2+24m+20}{m+2}\\=4m \left(m+2\right)\left( m^2+\frac{7m^2+24m+20}{m+2}\right)\\=4m \left(m+2\right)\left(m^2+7m+\frac{10m+20}{m+2}\right)\\=4m \left(m+2\right)\left(m^2+7m+10\right)\\=4m \left(m+2\right)\left(\left(m^2+2m\right)+\left(5m+10\right)\right)\\=4m \left(m+2\right)\left(m\left(m+2\right)+5\left(m+2\right)\right)\\=4m\left(m+2\right)\left(m+2\right)\left(m+5\right)\\=4m\left(m+2\right)^2\left(m+5\right)[/tex]
So this can be rewritten as:
[tex]=m\left(m+5\right)\left(2m+4\right)^2[/tex]
So this is option B. Hence this is the correct answer.
