Chapter SH, Problem 8.5.4EP

To determine

The factors of the given polynomial.

Answer to Problem 8.5.4EP

  $\left(1-3z\right)\left(1+3z\right)$

Explanation of Solution

Given:

The given polynomial is:

  $1-9z^2$

Calculation:

According to the theorem,

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

The factors of the given polynomial will be:

  $\begin{array}{l}=1-9z^2\\ ={\left(1\right)}^2-{\left(3z\right)}^2\\ =\left(1-3z\right)\left(1+3z\right)\end{array}$