Chapter R.6, Problem 120PE

For Exercise 115-120, factor the expressions over the set of complex numbers. For assistance, consider these examples.

$\begin{array}{l} ·\text{ In Section R}\text{.3 we saw that some expressions factor over the set of integers}\text{. For example: }\\ x^2-4=\left(x+2\right)\left(x-2\right).\\ ·\text{ Some expressions factor over the set of irrational numbers}\text{. For example: }\\ x^2-5=\left(x+\sqrt{5}\right)\left(x-\sqrt{5}\right).\\ ·\text{To factor an expression such as}{x}^2+4\text{, we need to factor over the set of complex numbers}\text{. For example,}\\ \text{verify that }{x}^2+4=\left(x+2i\right)\left(x-2i\right).\end{array}$

$\begin{array}{l}\text{a}\text{.}{x}^2-11\\ \text{b}\text{.}{x}^2+11\end{array}$