(x^3-1)(2x^2+3x+1)=0

Question

Please answer the question step by step and as soon as possible

Answer 1

x^3-1=(x-1)(x^2+x+1) and 2x^2+3x+1=(2x+1)(x+1).

So the complete factorisation and equation is (x-1)(x^2+x+1)(2x+1)(x+1)=0

The roots are x=1, x=-1/2, x=-1.

This can be taken further using complex numbers:

x^2+x+1=x^2+x+1/4+(1-1/4)=(x+1/2)^2+3/4=(x+1/2+i√3/2)(x+1/2-i√3/2) where i=√-1.

Additional roots are x=-1/2-i√3/2 and x=-1/2+i√3/2.