Chapter 4.1, Problem 13OE

To determine

The degree of the polynomial $ux-u^3{x}^2+u{x}^3-u^2$ by arranging terms in order of decreasing degree of $\left(x\right)$ .

Answer to Problem 13OE

The degree of the polynomial is 2.

Explanation of Solution

Given information: The given polynomial is,

  $ux-u^3{x}^2+u{x}^3-u^2\mathrm{....}\left(1\right)$

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

  $\begin{array}{c}ux-u^3{x}^2+u{x}^3-u^2=\left(u{x}^3\right)-\left(u^3{x}^2\right)+\left(ux\right)-\left(u^2\right)\mathrm{....}\left(\begin{array}{l}\text{Decreased }\\ \text{degree of }x\end{array}\right)\\ =u{x}^3-u^3{x}^2+ux-u^2\mathrm{......}\left(\text{Simplified}\right)\end{array}$

Now the terms of the simplified polynomial have degrees 4, 5, 2 and 2 respectively. Therefore the degree of the polynomial is 5.