To find the remainder when dividing a polynomial by a linear factor, we can use the Remainder Theorem. The theorem states that the remainder of the division of a polynomial f(x) by x – c is f(c).
In this case, we need to divide the polynomial f(x) = x³ – 2 by x – 1. According to the Remainder Theorem, we will evaluate f(1):
f(1) = (1)³ – 2
Calculating this gives:
f(1) = 1 – 2 = -1
Therefore, the remainder when x³ – 2 is divided by x – 1 is -1.
In conclusion, the remainder is -1.