The factor of:
[tex]2x^3-2[/tex] is:
[tex]x^2+x+1[/tex]
We are asked to find the factor of the algebraic expression which is given by:
[tex]2x^3-2[/tex]
we know that:
[tex]2x^3-2=2(x^3-1)[/tex]
which could again be written by:
[tex]2x^3-2=2(x-1)(x^2+x+1)[/tex]
Since,. we know that:
[tex]x^3-a^3=(x-a)(x^2+a^2+ax)[/tex]
Here a=1 hence,
[tex]x^3-1^3=x^3-1=(x-1)(x^2+x+1)[/tex]
Hence, the factors of:
[tex]2x^3-2[/tex] are [tex]2,(x-1)\ and\ x^2+x+1[/tex]
Hence, the answer is:
[tex]x^2+x+1[/tex]
