Question

The factor of the determinant

$\left|\begin{array}{ccc}x& 5& 2\\ x^2& 9& 4\\ x^3& 16& 8\end{array}\right|$ is (x - .......)

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B

2

As explained in the factor theorem the value of the variable x which makes the determinant zero is called the factor of the determinant.

In the above question, we can see that if we put x=2 the elements of the first columns becomes 2, 4 and 8 which is same as the third column. And as we have seen before, when two rows or columns are same the value of the determinant is 0. So (x-2) is the factor of the above determinant.