ANSWER
The correct choice is D.
EXPLANATION
Let
[tex]f( x) = 3 {x}^{3} - 4 {x}^{2} - 13x - 6[/tex]
According to the Factor Theorem, if x-a is a factor of f(x), then f(a)=0.
For option A,
[tex]f( - 6) = 3 {( - 6)}^{3} - 4 {( - 6)}^{2} - 13( - 6) - 6[/tex]
[tex]f( - 6) = - 720[/tex]
Hence x+6 is not a factor.
For option B,
[tex]f( - 3) = 3 {( - 3)}^{3} - 4 {( - 3)}^{2} - 13( - 3) - 6[/tex]
[tex]f( - 3) = - 84[/tex]
x+3 is also not a factor.
For option C,
[tex]f( 4) = 3 {( 4)}^{3} - 4 {( 4)}^{2} - 13( 4) - 6[/tex]
[tex]f(4) = 70[/tex]
Option D,
[tex]f( - 1) = 3 {( - 1)}^{3} - 4 {( - 1)}^{2} - 13( - 1) - 6[/tex]
[tex]f( - 1) = - 3 - 4 + 13 - 6[/tex]
[tex]f( - 1) = 0[/tex]
x+1 is a factor.
