Answer: The complete factorization of the given expression is [tex]3(x-3)(x+6).[/tex]
Step-by-step explanation: We are given to factor completely the following quadratic expression :
[tex]E=3x^2+9x-54\\\\\Rightarrow E=3(x^2+3x-18)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To completely factor expression (i), we need two integers with sum 3 and product -18. Those two integers are 6 and -3.
The complete factorization of expression (i) is as follows :
[tex]E\\\\=3(x^2+3x-18)\\\\=3(x^2+6x-3x-180)\\\\=3(x(x+6)-3(x+6))\\\\=3(x-3)(x+6).[/tex]
Thus, the complete factorization of the given expression is [tex]3(x-3)(x+6).[/tex]
