ANSWER
The complete factorization is
[tex] 2 {x}^{2} - x - 6 = (2x + 3)(x - 2)[/tex]
EXPLANATION
The given expression is
[tex]2 {x}^{2} - x - 6[/tex]
This is a quadratic trinomial with,
[tex]a=2,b=-1,c=-6[/tex]
[tex]ac = - 12[/tex]
Two factors of -12 that adds up to -1 are
[tex] - 4,3[/tex]
We split the middle term to obtain,
[tex]2 {x}^{2} - 4x + 3x- 6[/tex]
We factor to get,
[tex]2x(x - 2) + 3(x - 2)[/tex]
We factor further to get,
[tex] \therefore2 {x}^{2} - x - 6 = (2x + 3)(x - 2)[/tex]
