what is the factor of a^4-7a^2+9 ?

Answer 1

a^4-7a^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 (√13-1)

Makes things kind of nasty, the factors are

1/16 (±2x + √13 ± 1)

where all 4 combinations of + and - are used.

Answer 2

Hint:
substitute u=a^2, then
a^4-7a^2+9
=u^2-7u+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.