Question

Find the factors of


x^3+2x^2+2x+1​

Answer 1

Answer:

ANSWER

x3+2x2+2x+1=0

(x3+1)+2x(x+1)=0

(x+1)(x2−x+1)+2x(x+1)=0

(x+1)(x2+x+1)=0

x=−1 and x2+x+1=0 implies x=w,w2 where w and w2 are cube roots of unity.

Now x=−1 does not satisfy the second equation,

Hence the common roots are w,w2, 

since, w1988+w130++1=1.w2+1.w+1=0

and w2×1988+w2×130++1=1.w+1.w2+1=0. since, (w3=1.)

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