math
posted by jerroyle .
what is the factor of a^47a^2+9 ?

a^47a^2+9
a^2 = (7±√13)/2
Now it gets tricky:
7+√13 = (1+2√13+13)/2 = (1+√13)^2/2
So, if
a^2 = (7+√13)/2 = (1+√13)^2/4
a = ±1/2 (√13+1)
and
a = ±1/2 (√131)
Makes things kind of nasty, the factors are
1/16 (±2x + √13 ± 1)
where all 4 combinations of + and  are used. 
Hint:
substitute u=a^2, then
a^47a^2+9
=u^27u+9
and try to factorize.
However, check you question to see if there is a typo. The above expression in u does not have rational factors.