Answer: The correct option is
(C) [tex]3x(x^2-5)(3x+4).[/tex]
Step-by-step explanation: We are given to completely factor the following bi quadratic expression :
[tex]E=9x^4+12x^3-45x^2-60x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Since the given expression does not contain the constant term, so we will take out the x-term common and then will try to factorize the remaining cubic expression.
The factorization of expression (i) is as follows :
[tex]E\\\\=9x^4+12x^3-45x^2-60x\\\\=3x(3x^3+4x^2-15x-20)\\\\=3x(x^2(3x+4)-5(3x+4))\\\\=3x(x^2-5)(3x+4).[/tex]
Thus, the required factored form of the given expression is [tex]3x(x^2-5)(3x+4).[/tex]
Option (C) is CORRECT.
