Question

How do you factor `25x^2 + 49`?

Answer 1

That depends on what numbers we are using.

This binomial is irreducible (cannot be factored) over the real numbers.

If we are working with polynomials over the complex numbers, then this is a difference of squares and can be factored using `-49 = (7i)^2`, so

`25x^2 + 49 = 25x^2 -(-49)`

`=(5x+7i)(5x-7i)`