To find the remainder when dividing a polynomial by a linear term, we can use the Remainder Theorem. The theorem states that the remainder of the division of a polynomial f(x) by the linear polynomial x – c is f(c).
In this case, our polynomial is f(x) = x³ – 2 and we are dividing by x – 1. Thus, we will find f(1) to determine the remainder:
f(1) = (1)³ – 2 = 1 – 2 = -1
Therefore, the remainder when x³ – 2 is divided by x – 1 is -1.