Answer and Step-by-step explanation:
To determine if (x - 1) is a factor of x^3 - x^2 + x + 8, we can use the Factor Theorem. The Factor Theorem states that if f(x) is a polynomial and f(a) = 0, then (x - a) is a factor of f(x).
In this case, f(x) = x^3 - x^2 + x + 8 and a = 1. So, we can evaluate f(1) to see if it equals 0:
f(1) = (1)^3 - (1)^2 + (1) + 8 = 1 - 1 + 1 + 8 = 9
Since f(1) ≠ 0, we can conclude that (x - 1) is not a factor of x^3 - x^2 + x + 8.