Question

Factor the expression over the complex numbers.x2 + 25Enter your answer in the box.Basic

Answer 1

Factor the expression;

`x^2+25`

First of all, we take note of the following;

`\begin{gathered} x^2=x\cdot x \\ 25=5\cdot5 \\ -i^2=1 \end{gathered}`

Therefore, we'll now have;

`\begin{gathered} x^2+25=x^2+25(-i^2) \\ x^2+25=x^2-25i^2 \\ \text{Note also that;} \\ a^2-b^2=(a+b)(a-b) \\ \text{Therefore;} \\ x^2-25i^2=(x-5i)(x+5i) \end{gathered}`

ANSWER:

`(x-5i)(x+5i)`