Final answer:
A(x), C(x), and D(x) are the polynomials that have (x-3) as a factor.
Step-by-step explanation:
In order to determine if (x-3) is a factor of a polynomial, we can substitute x=3 into the polynomial and see if the result is equal to 0. Let's check each polynomial:
(A) A(x) = x^3 - 2x^2 - 4x + 3 --> A(3) = 3^3 - 2(3)^2 - 4(3) + 3 = 27 - 18 - 12 + 3 = 0, so (x-3) is a factor of A(x).
(B) B(x) = x^3 + 3x^2 - 2x - 6 --> B(3) = 3^3 + 3(3)^2 - 2(3) - 6 = 27 + 27 - 6 - 6 = 42, so (x-3) is not a factor of B(x).
(C) C(x) = x^4 - 2x^3 - 27 --> C(3) = 3^4 - 2(3)^3 - 27 = 81 - 54 - 27 = 0, so (x-3) is a factor of C(x).
(D) D(x) = x^4 - 20x - 21 --> D(3) = 3^4 - 20(3) - 21 = 81 - 60 - 21 = 0, so (x-3) is a factor of D(x).
Therefore, the polynomials that have (x-3) as a factor are A(x), C(x), and D(x).