Chapter R - Review of Basic Concepts - R.4 Factoring Polynomials - R.4 Exercises - Page 43: 9

B

Note that $x^4=(x^2)^2$ and $1=1^2$. Thus, the given binomial can be written as: $=(x^2)^2-1^2$ Factor using the formula $a^2-b^2=(a+b)(a-b)$ where $a=x^2$ and $b=1$ to obtain: $=(x^2+1)(x^2-1)$ Factor the second binomial using the same formula with $a=x$ and $b=1$ to obtain: $=(x^2+1)(x+1)(x-1)$ Therefore, the answer is Option B.