Question

Which of the following is a factor of 6x2 + 2x − 21?

4x − 3
2x + 7
6x − 3
None of the above

Answer 1

ANSWER

None of the above

Step-by-step explanation

The quadratic expression given to us is


`6 {x}^(2) + 2x - 21`

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`
We have,

`a=6,b=2,c=-21`


The discriminant is given by,


`D = {b}^(2) - 4ac`

Thus


`D = {2}^(2) - 4(6)( - 21)`



`D = 4 + 504 = 508`

Since 508 is not a perfect square, the expression



`6 {x}^(2) + 2x - 21`
has no rational factors.


Therefore D is the correct answer.