You can do defactoring of the given polynomial in simpler polynomials to get it as a product of prime polynomials (assuming that it itself is not a prime polynomial)
The product of prime polynomial which forms the given polynomial is given by
Option B: [tex]4x^2(2x-3)(x+6)[/tex]
Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called prime polynomial.
(it is necessary that no factors exists having their coefficients are still integers and they're of lower degree)
We can try defactoring the given polynomial in simpler polynomials.
The given polynomial is
[tex]8x^4 + 36x^3 - 72x^2\\[/tex]
Factorizing it can be done as
[tex]\begin{aligned} 8x^4 + 36x^3 - 72x^2 &= 4x^2(2x^2 + 9x - 18)\\&= 4x^2(2x^2 + 12x - 3x - 18)\\&= 4x^2(2x(x+6) -3(x+60))\\&= 4x^2(x+6)(2x-3)\\&=4x^2(2x-3)(x+6)\\\end{aligned}[/tex]
Thus,
The product of prime polynomial which forms the given polynomial is given by
Option B: [tex]4x^2(2x-3)(x+6)[/tex]
Learn more about prime polynomials here:
https://brainly.com/question/10717989