Factorize this expression

There are no rational roots to this equation. The only possible rational roots would be -5, -1, 1 and 5 since they must be factors of 5 divided by factors of 1.

You can factor this into two quadratics and use the quadratic equation to get the roots.

(a^2 - 3a + 1)(a^2 - 3a + 5)

take a^4 - 6a^3 +15a^2 - 18a + 5
and set equal to (a^2+n1a+m1)(a^2+n2a+m2)

Two things you know right off the bat
m1*m2=5
n1+n2=-6
if this is factorable easily then m1=+/-1 and m2=+/-5
now you also may know that m1+m2+n1n2=15
so set m1=1 and m2=5 so n1n2=9
as n2n2=9 and n1+n2=-6 then n2=-3 and n2=-3

Now you've factored the quartic into two quadratics
a^4 - 6a^3 +15a^2 - 18a + 5 =(a^2-3a+1)(a^2-3a+5)
You can factor this using the quadratic formula

Hint
you will get four real roots
or
two real and two imaginary roots
or
four imaginary roots

Rap

please can you explain how it came