polynomial question

Q.1 If x - 1 and 2x - 3 are factors of f(x) = 6x^3 = px^2 + qx - 15 , which of the following is also a factor of f(x) ?
A. 3x - 5
B. 3x + 5
C. 6x - 5
D. 6x + 5
x - 1 and 2x - 3 are factors of f(x) = 6x^3 = px^2 + qx - 15
f(x)=(x-1)(2x-3)c(x)
6x^3 = px^2 + qx - 15 =(2x^2-5x+3)c(x)
where c(x)=ax+b
Compare the constant term=-5
Compare x^3 term a=3
So the answer is A (3x-5)
Q.2 Let f(x) be a polynomial . If f(0) = f(2) = 0 which of the following must not be a factor of f(x)
I. x
II. x - 2
III. x + 2
A. I only
B. II only
C. III only
D. None of the above
We have x and (x-2) is a factor of f(x)
We do not know x+2 is or is not a factor of f(x)
So the answer is D. None of the above