Chapter 1.3, Problem 110PE

For Exercises 105–110, factor the expressions over the set of complex numbers. For assistance, consider these examples.

In Chapter R we saw that some expressions factor over the set of integers. For example: $x^2-4=\left(x+2\right)\left(x-2\right)$.

Some expressions factor over the set of irrational numbers. For example: $x^2-5=\left(x+\sqrt{5}\right)\left(x-\sqrt{5}\right)$.

To factor an expression such as x2 1 4, we need to factor over the set of complex numbers. For example, verify that $x^2+4=\left(x+2i\right)\left(x-2i\right)$.

a. $x^2-11$

b. $x^2+11$