What is the quotient when 2x^3-1 is divided by x - 1?

Step-by-step explanation:

Use synthetic division:

The coefficients of 2x^3 - 1 are {2, 0, 0, -1}.  Setting up synthetic division, we get:

1    /    2    0    0    -1

                2     2    2

          2     2    2     1

Note that the remainder is 1.  The same result would be obtained through long division.

The quotient is 2x^2 + 2x + 2 with a remainder of 1.