ANSWER
None of the above
EXPLANATION
The quadratic expression given to us is
![6 {x}^{2} + 2x - 21](/tpl/images/0492/8987/28ed3.png)
If the discriminant of this quadratic expression is a perfect square, then it has rational factors,
If we compare the above expression to the general quadratic expression,
![a {x}^{2} + bx + c](/tpl/images/0492/8987/fedc5.png)
We have,
![a=6,b=2,c=-21](/tpl/images/0492/8987/22b59.png)
The discriminant is given by,
![D = {b}^{2} - 4ac](/tpl/images/0492/8987/e97af.png)
Thus
![D = {2}^{2} - 4(6)( - 21)](/tpl/images/0492/8987/619f2.png)
![D = 4 + 504 = 508](/tpl/images/0492/8987/df4a1.png)
Since 508 is not a perfect square, the expression
![6 {x}^{2} + 2x - 21](/tpl/images/0492/8987/28ed3.png)
has no rational factors.
Therefore D is the correct answer.