Question

find the quotient of $-20y^3 - 40y^2$ divided by $-5y^2$.

Explanation:

Step1: Split the polynomial

We can split the division of the polynomial by the monomial into two separate divisions: $\frac{-20y^{3}}{-5y^{2}}+\frac{-40y^{2}}{-5y^{2}}$.

Step2: Divide the coefficients and variables

For the first term, divide the coefficients: $\frac{-20}{-5} = 4$, and divide the variables using the rule of exponents $a^{m}\div a^{n}=a^{m - n}$: $\frac{y^{3}}{y^{2}}=y^{3-2}=y$. So the first term is $4y$.
For the second term, divide the coefficients: $\frac{-40}{-5}=8$, and divide the variables: $\frac{y^{2}}{y^{2}} = y^{2 - 2}=y^{0}=1$. So the second term is $8$.

Step3: Combine the terms

Combine the two terms we got: $4y + 8$.

Answer:

$4y + 8$