Question

The product of two numbers is $-14m^6{n}^3-21m^4{n}^5+7m^5{n}^4$. If one number is $7m^2{n}^2$, then find the other number.

• A. $2m^{4}n+3m^2{n}^3+m^3{n}^2$
• B. $-2m^{4}n-3m^2{n}^3+m^3{n}^2$
• C. $2m^{4}n-3m^2{n}^3+m^3{n}^2$
• D. $-2m^{4}n-3m^2{n}^3-m^3{n}^2$

Answer 1

The correct option is B

$-2m^{4}n-3m^2{n}^3+m^3{n}^2$

Tthe product of two numbers is $-14m^6{n}^3-21m^4{n}^5+7m^5{n}^4$.

One number = $7m^2{n}^2$

Then second number is $\frac{-14m^6{n}^3-21m^4{n}^5+7m^5{n}^4}{7m^2{n}^2}$

We shall perform the above division as follows:

$\frac{-14m^6{n}^3-21m^4{n}^5+7m^5{n}^4}{7m^2{n}^2}$

= $\frac{-14m^6{n}^3}{7m^2{n}^2}-\frac{21m^4{n}^5}{7m^2{n}^2}+\frac{7m^5{n}^4}{7m^2{n}^2}$

= $-2m^{4}n-3m^2{n}^3+m^3{n}^2$