what is best choice for these questions?

Question

A polynomial function is defined as f(x) = 3x³ + bx² + cx + d, where b, c, and d are integers. Given that f(3) = 0, which of the following is a possible value of d?

1. A.8
2. B.9
3. C.10
4. D.11

The function g(x) is a polynomial function. The remainder of , where x ≠ 6, is 18. What is the value of g(6)?

1. A.18
2. B.12
3. C.6
4. D.3

Answer 1

1. Plugging in x=3 gives f(3) = 81 + 9b + 3c + d = 0. Since b, c, and d are integers, and all terms besides d are divisible by 3, it follows that d must also be divisible by 3. The only choice is B.
2. g(x)/(x - 6) = Z(x) + 18/(x - 6), where Z is a function of x. Cross multiplying gives g(x) = (x - 6)Z(x) + 18. Therefore, g(6) = 0 + 18 = 18.

Answer 2

For the first one:

If f(3) = 0, that means that x - 3 is one factor of the polynomial. Therefore, the constant term (d) must be a multiple of 3.

Answer is B: 9