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

Apr 14, 2016

Answer:

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:

$5 {a}^{2} + {b}^{2} = {\left(\sqrt{5} a\right)}^{2} - {\left(b i\right)}^{2} = \left(\sqrt{5} a - b i\right) \left(\sqrt{5} a + b i\right)$

Alternatively, if we were told that $b \ge 0$ then we could write

$5 {x}^{2} + b = {\left(\sqrt{5} a\right)}^{2} - {\left(\sqrt{b} i\right)}^{2} = \left(\sqrt{5} a - \sqrt{b} i\right) \left(\sqrt{5} a + \sqrt{b} i\right)$