Chapter 8.5, Problem 2CCYP

To determine

The factorization of the polynomial.

Answer to Problem 2CCYP

  $\left(9-x^2\right)\left(9+x^2\right)$

Explanation of Solution

Given:

The given polynomial is:

  $81-x^4$

Calculation:

It is known that,

  $a^2-b^2=\left(a+b\right)\left(a-b\right)$

The given polynomial can be written as:

  $\begin{array}{l}=81-x^4\\ ={\left(9\right)}^2-{\left(x^2\right)}^2\\ =\left(9-x^2\right)\left(9+x^2\right)\end{array}$