Factor:
$\displaystyle 27x^2+64$
I am completely lost...
$\displaystyle
27x^2+64
$
this is a binomial expression- an expression with two terms, the variable, x is only present in the first term and thus you cannot factor it. We are only left with the constants 27 and 64. These numbers do not have a common favtor hence we cannot factor again. Thus the expression canot be factored
I'll assume you're required to factorise over the complex number field. Otherwise, as has been previously correctly noted, it can't be done and the question is pointless.
Recall: $\displaystyle A^2 + B^2 = (A + iB)(A - iB)$.
In your case, $\displaystyle A = \sqrt{27} \, x = 3 \sqrt{3} \, x$ and B = 8 ....