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

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Answer 1 · 2016-04-14T21:22:47

This expression cannot be simplified further.

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

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

How do you factor completely 5a^2 + b5a^2 + b?