Answer: The HCF of these three polynomials is (x^2 - 2x + 4)(x - 1) = x^3 - 3x^2 + 5x - 4.
Explanation:
The HCF of these three polynomials is the product of all the common factors shared between them. In this case, the common factors are x^2 - 2x + 4, which appears in both x^3 + 8 and x^2 - 2x + 4, and x - 1, which appears in x^2 - 2x + 4. Therefore, the HCF of these three polynomials is (x^2 - 2x + 4)(x - 1) = x^3 - 3x^2 + 5x - 4.