Question

One of the factors of the determinant

$\left|\begin{array}{ccc}x& 5& 3\\ x^2& 9& 9\\ x^3& 16& 27\end{array}\right|$ is

• A. $x-1$
• B. $x-2$
• C. $x-3$
• D. $x-4$

Answer 1

The correct option is C

$x-3$

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 $x=3$ the elements of the first columns becomes 3, 9 and 27 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 $x-3$ is the factor of the above determinant.