How do you factor completely 5a^2 + b5a2+b?

1 Answer
George C.
Apr 14, 2016

This expression cannot be simplified further.

Explanation:

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

If the second term was b^2b2 rather than bb, 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)5a2+b2=(√5a)2−(bi)2=(√5a−bi)(√5a+bi)

Alternatively, if we were told that b >=0b≥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)5x2+b=(√5a)2−(√bi)2=(√5a−√bi)(√5a+√bi)

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