Chapter 8, Problem 33PT

To determine

To find the factor of $x^4-1.$

Answer to Problem 33PT

Option A: $(x^2-1)$

Explanation of Solution

Given:

Expression: $x^4-1$

Formula used:

  $(a+b)(a-b)=a^2-b^2$

Calculation:

Consider the given expression,

  $\begin{array}{l}\Rightarrow x^4-1\\ \Rightarrow x^4-1^2\\ $ \Rightarrow {(x^2)}^2-1^2$\end{array}$

Using the above formula,

  $\Rightarrow (x^2-1)(x^2+1)$

So, the factors of the expression are $(x^2-1)$ and $(x^2+1).$

The above factors matches with a factor present in option A.

Conclusion:

Therefore, option A is correct.