Question

Find the degree of the quotient when $4x^3{y}^4{z}^5$ is divided by $16x^2{y}^2{z}^2$.

• A. $12$
• B. $6$
• C. $4$
• D. $\frac{1}{4}$
  

Answer 1

The correct option is B $6$

We need to divide $4x^3{y}^4{z}^5$ by $16x^2{y}^2{z}^2$.

This can be done as:
$\frac{4x^3{y}^4{z}^5}{16x^2{y}^2{z}^2}$

$=\frac{4x^{3-2}{y}^{4-2}{z}^{5-2}}{4\times 4}$ ($\because \frac{a^m}{a^n}=a^{m-n}$)

$=\frac{x{y}^2{z}^3}{4}$

The quotient obtained when $4x^3{y}^4{z}^5$ is divided by $16x^2{y}^2{z}^2$ is $\frac{x{y}^2{z}^3}{4}$.

The degree of the quotient is obtained by adding the exponents of all the variables present in it.

Degree of $\frac{x{y}^2{z}^3}{4}=1+2+3$
$=6$

The degree of the quotient, i.e., $\frac{x{y}^2{z}^3}{4}$ is $6$.

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