Chapter 3.3, Problem 4QR

To determine

The expression by writing it as a sum of powers of x .

Answer to Problem 4QR

The required expression is $\frac{3}{2}{x}^2-x+2x^{-2}$ .

Explanation of Solution

Given information:

The expression $=\frac{3x^4-2x^3+4}{2x^2}$

Formula used:

Property of negative exponent:

  $\frac{1}{x^n}=x^{-n}$

Calculation:

The given expression is $\frac{3x^4-2x^3+4}{2x^2}$ .

To write the above expression as a sum of powers of x , use the property of negative exponent.

  $\begin{array}{c}\frac{3x^4-2x^3+4}{2x^2}=\frac{3x^4}{2x^2}-\frac{2x^3}{2x^2}+\frac{4}{2x^2}\\ =\frac{3}{2}{x}^2-x+\frac{2}{x^2}\\ =\frac{3}{2}{x}^2-x+2x^{-2}\end{array}$

Hence, the required expression is $\frac{3}{2}{x}^2-x+2x^{-2}$ .