Question

How do you factor completely `5a^2 + b`?

Answer 1

This expression cannot be simplified further.

Explanation:

Unless we are given extra information (e.g. `b = -5`), then this expression cannot be factored further.

If the second term was `b^2` rather than `b`, then it would be possible to factor using Complex coefficients:

`5a^2+b^2 = (sqrt(5)a)^2-(bi)^2 = (sqrt(5)a-bi)(sqrt(5)a+bi)`

Alternatively, if we were told that `b >=0` then we could write

`5x^2+b = (sqrt(5)a)^2-(sqrt(b)i)^2 = (sqrt(5)a-sqrt(b)i)(sqrt(5)a+sqrt(b)i)`