We have to take out the greatest common factor from the given polynomial to factorize the expression. If you observe the terms of the polynomial, the greatest factor that is common to all the terms is [tex]4 x^{4} [/tex]. So taking it out as common, the factorization of the polynomial will be:
[tex]16 x^{9} -36 x^{5}-8 x^{4} \\ \\
=4 x^{4}(4 x^{5}-9x-2) [/tex]
So the option C gives the correct answer
