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

1 Answer
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:

#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)#