The given expression is
[tex]11x^2-44x-231[/tex]
Since the greatest common factor of 11, 44, 231 is 11, then divide each term by 11 to take it as a common factor
[tex]11(\frac{11x^2}{11}-\frac{44x}{11}-\frac{231}{11})=11(x^2-4x-21)[/tex]
Now, we will factorize the trinomial into 2 factors
Since
[tex]\begin{gathered} x^2=(x)(x) \\ -21=(-7)(3) \\ -4x=(-7)(x)+(3)(x) \end{gathered}[/tex]
Then the 2 factors are (x - 7)(x + 3)
[tex]11(x^2-4x-21)=11(x-7)(x+3)[/tex]
