Answer :

Given, a second degree polynomial x2 + x + 1


Need to prove the given equation cannot be written as product of first degree polynomial


we know that a polynomial equation of degree 2, x2 + (a + b)x + ab can be written as (x + a)(x + b)


Here, x2 + x + 1 is written as x2 + (a + b)x + ab


coefficient on either side are equal, we get


a + b = 1 and ab = 1


We need to find the values of a, b such that it satisfies the given equation to get the factors of first degree polynomial


Since, a + b = 1 and ab = 1 it is not possible to find out the values of a, b which satisfy the equation x2 + x + 1


Hence, x2 + x + 1 cannot be splited into factors of first degree polynomial


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