the given polynomial isndivisible by------------------------------------where w is cube root of unity

On substituting x= w in the given polynomial we get 0. Hence, x-w is a factor of the given polynomial.

Similarly, on substituting x= w² in the given polynomial we get 0. Hence, x-w² is also a factor of the given polynomial.

Since both x-w and x-w² are factors of the given polynomial, (x-w)(x-w²) is also a factor of the given polynomial. So, the given polynomial is divisible by (x-w)(x-w²).

Hence, the correct answer is option D.

 

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