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Which of the following is a factor of 2x3 – 2?


x + 1


x2 + x + 1


x2 + 2x + 1


None of the above

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Answer:

The factor of:

               \(2x^3-2\) is:

         \(x^2+x+1\)

Step-by-step explanation:

We are asked to find the factor of  the algebraic expression which is given by:

               \(2x^3-2\)

we know that:

\(2x^3-2=2(x^3-1)\)

which could again be written by:

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

Since,. we know that:

\(x^3-a^3=(x-a)(x^2+a^2+ax)\)

Here a=1 hence,

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

Hence, the factors of:

\(2x^3-2\) are \(2,(x-1)\ and\ x^2+x+1\)

               Hence, the answer is:

                      \(x^2+x+1\)

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