Answer: The correct option is
(B) [tex]3x(x+3)(x-2).[/tex]
Step-by-step explanation: We are given to completely factor the following cubic expression :
[tex]E=3x^3+3x^2-18x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Since the given expression does not contain the constant term, so we will take out the x-term and then factorize the remaining quadratic expression.
The factorization of the given expression (i) is as follows :
[tex]E\\\\=3x^3+3x^2-18x\\\\=3x(x^2+x-6)\\\\=3x(x^2+3x-2x-6)\\\\=3x(x(x+3)-2(x+3))\\\\=3x(x+3)(x-2).[/tex]
Thus, the complete factored form of the given expression is [tex]3x(x+3)(x-2).[/tex]
Option (B) is CORRECT.
