Question

Find the quotient when $9p^5{q}^5-15p^3{q}^3+27p^2{q}^2$ is divided by $-3pq$.

• A. $-3p^4{q}^4+5p^2{q}^2+9pq$
• B. $-3p^4{q}^4+5p^2{q}^2-9pq$
• C. $3p^4{q}^4+5p^2{q}^2-9pq$
• D. $3p^4{q}^4-5p^2{q}^2+9pq$

Answer 1

The correct option is B $-3p^4{q}^4+5p^2{q}^2-9pq$

We need to find the quotient when $9p^5{q}^5-15p^3{q}^3+27p^2{q}^2$ is divided by $-3pq$.

This means that we need to find the value of
$\frac{9p^5{q}^5-15p^3{q}^3+27p^2{q}^2}{-3pq}$

This can be evaluated as:

$\frac{9p^5{q}^5-15p^3{q}^3+27p^2{q}^2}{-3pq}$

$=\frac{9p^5{q}^5}{-3pq}+\frac{-15p^3{q}^3}{-3pq}+\frac{27p^2{q}^2}{-3pq}$

$=-3p^{5-1}{q}^{5-1}+5p^{3-1}{q}^{3-1}$
$-9p^{2-1}{q}^{2-1}$ ($\because \frac{a^m}{a^n}=a^{m-n}$)

$=-3p^4{q}^4+5p^2{q}^2-9pq$


The value of the quotient when $9p^5{q}^5-15p^3{q}^3+27p^2{q}^2$ is divided by $-3pq$ is $-3p^4{q}^4+5p^2{q}^2-9pq$.

Therefore, option (b.) is the correct answer.