Question 1206040
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There might be a typo with your question.


I plugged this into WolframAlpha
<a href="https://www.wolframalpha.com/input?i=determinant+%7B%7B+b+-+c+%2C+c+-+a+%2C+c+%7D%2C%7B+c+%2C+b+-+x+%2C+a+%7D%2C%7B+c+%2C+a+%2C+c+-+x+%7D%7D">https://www.wolframalpha.com/input?i=determinant+%7B%7B+b+-+c+%2C+c+-+a+%2C+c+%7D%2C%7B+c+%2C+b+-+x+%2C+a+%7D%2C%7B+c+%2C+a+%2C+c+-+x+%7D%7D</a>
and the result it produces is
-a^2b+3ac^2-acx+b^2c-b^2x-2bc^2+bx^2-c^3+3c^2x-cx^2


Unfortunately, none of those terms cancel out so the whole thing does not go to zero.
I would carefully double-check to make sure you did not make an error typing in the expression. Also, I recommend contacting your teacher for further clarification. 
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