To factor out the expression we look for number which is divisible by every term in our case it is 3n^2:
3n^4+21n^3+27n^2
we first begin by factoring out 3n^2, this will give us;
3n^2(n^2+7n+9)
hence, since we cannot factorize the quadratic expression the answer remains to be:
3n^2(n^2+7n+9)