Question

$If$ $n$ is a natural number then$\left|\begin{array}{ccc}1& 1& 1\\ a& b& c\\ a^{n+2}& b^{n+2}& c^{n+2}\end{array}\right|$ has a factor given by

• A. (a-b) (b-c) (a+c)
• B. (a+b) (b+c) (c+a)
• C. (a-b) (b-c) (c-a)
• D. abc

Answer 1

The correct option is C (a-b) (b-c) (c-a)

Setting a= b makes a-b a factor,
similarly b-c, c-a
thus $(a-b)(b-c)(c-a)$ is a factor