Question

Find the quotient when $4a^3{b}^4+6a^7{b}^3-8b^2{a}^5$ is divided by $-2ab$.

• A. $-2p^2{b}^3-3a^6{b}^2+4a{b}^4$
• B. $2p^2{b}^3-3a^6{b}^2+4a^{4}b$
• C. $-2p^2{b}^3+3a^6{b}^2+4a^{4}b$
• D. $-2p^2{b}^3-3a^6{b}^2+4a^{4}b$

Answer 1

The correct option is D $-2p^2{b}^3-3a^6{b}^2+4a^{4}b$

We need to find the quotient when $4a^3{b}^4+6a^7{b}^3-8b^2{a}^5$ is divided by $-2ab$.

This means that we need to find the value of
$\frac{4a^3{b}^4+6a^7{b}^3-8b^2{a}^5}{-2ab}$.

This can be evaluated as:

$\frac{4a^3{b}^4+6a^7{b}^3-8b^2{a}^5}{-2ab}$

$=\frac{4a^3{b}^4}{-2ab}+\frac{6a^7{b}^3}{-2ab}+\frac{-8b^2{a}^5}{-2ab}$

$=-2a^{3-1}{b}^{4-1}-3a^{7-1}{b}^{3-1}+4a^{5-1}{b}^{2-1}$
($\because \frac{a^m}{a^n}=a^{m-n}$)

$=-2a^2{b}^3-3a^6{b}^2+4a^{4}b$


The value of the quotient when $4a^3{b}^4+6a^7{b}^3-8b^2{a}^5$ is divided by $-2ab$ is $-2a^2{b}^3-3a^6{b}^2+4a^{4}b$.