Chapter 4.1, Problem 8WE

To determine

The degree of the polynomial $7x{y}^2{z}^3-4x{y}^2{z}^3+2x^{2}y{z}^2-3x{y}^2{z}^3$ by arranging terms in order of decreasing degree of $\left(x\right)$ and simplify.

Answer to Problem 8WE

The degree of the polynomial is 5.

Explanation of Solution

Given information: The given polynomial is,

  $7x{y}^2{z}^3-4x{y}^2{z}^3+2x^{2}y{z}^2-3x{y}^2{z}^3\mathrm{....}\left(1\right)$

Calculation: The polynomial (1) can be written as,

  $\begin{array}{c}7x{y}^2{z}^3-4x{y}^2{z}^3+2x^{2}y{z}^2-3x{y}^2{z}^3=\left(2x^{2}y{z}^2\right)+\left(7x{y}^2{z}^3-4x{y}^2{z}^3-3x{y}^2{z}^3\right)\\ =\left(2x^{2}y{z}^2\right)+\left(0\right)\mathrm{......}\left(\text{Simplified}\right)\\ =2x^{2}y{z}^2\end{array}$

After simplification the polynomial (1) is reduced to $2x^{2}y{z}^2$ which has the degree 5. Therefore the degree of the polynomial is 5.