Chapter 12, Problem 3STP

To determine

To find: the non factor of the expression.

Answer to Problem 3STP

The $x^2-3$ is not a factor of expression.

Explanation of Solution

Given information:

The expression is $x^4-6x^2-27$ .

Calculation:to find the non-factor first find the factors of expression,

  $\begin{array}{l}{x}^4-6x^2-27=0\\ x^4-9x^2+3x^2-27=0\text{ [break the }-6x^2]\\ x^2\left(x^2-9\right)+3\left(x^2-9\right)=0\text{ [simplify]}\\ \left(x^2+3\right)\left(x^2-9\right)=0\text{ [factors]}\end{array}$

Thus, $x^2-3$ Is not a factor of expression.