factorize: x^6-7x^3-8 .

Answers (1)

solution: we have ,

x^6-7x^3-8

=y^2-7y-8 ,    where y=x^3

=(y^2-8y)+(y-8)=y(y-8)+1(y-8)

=(y-8)(y+1)=(x^3-8)(x^3+1)

=(x^3-2^3)(x^3+1^3)=(x-2)(x^2+2x+4)(x+1)(x^2-x+1)

=(x-2)(x+1)(x^2+2x+4)(x^2-x+1)

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