X+4 divided by x^2+16

Why can't it be simplified?

Let's try to simplify x^2 + 16. It's a sum of two squares:

x^2 + 16 = 0

x^2 = - 16

The problem is, we can't take a square root of a negative. This is where imaginary numbers come in.

Remember that square roots have a plus or minus symbol outside:

±√-16 = ±4i

Our two roots are 4i and - 4i. Therefore, the trinomial simplifies to:

(x + 4i) (x - 4i)

If we attempt to divide x + 4 by these two binomials, we will find that 4 and 4i are not like terms. Therefore, we can't simplify this expression.