Final answer:
By substituting x=1 into the polynomial and showing that f(1) = 0, we can confirm that (x-1) is a factor of the polynomial according to Factor Theorem.
Step-by-step explanation:
To show that (x-1) is a factor of the given polynomial f(x) = 2x^3 - 30c^2 + 70c - 6, we need to utilize the Factor Theorem which states that if a polynomial f(x) has a factor (x - a), then f(a) = 0. In this case, we want to prove that f(1) = 0.
Substitute x = 1 into the polynomial:
f(1) = 2(1)^3 - 30(1)^2 + 70(1) - 6
f(1) = 2 - 30 + 70 - 6
f(1) = 36 - 36
f(1) = 0
Since f(1) equals zero, (x - 1) is indeed a factor of f(x).