Let f(x) be a polynomial. If f(3)=0 and f(-2)=0, which of the following must be a factor/factors of f(x)?
A. x+2 and x-3
B. x+2 and x+3
C. x-2 and x-3
D. x-2 and x+3

@Callisto

Question

Let f(x) be a polynomial. If f(3)=0 and f(-2)=0, which of the following must be a factor/factors of f(x)?
A. x+2 and x-3
B. x+2 and x+3
C. x-2 and x-3
D. x-2 and x+3

@Callisto

anonymous · Answer

@Callisto I am very weak in polynomials....

callisto · Answer

If f(a) = 0, then x-a is a factor of f(x), by the factor theorem.

anonymous · Answer

oh, then it's x+2, x-3....?

callisto · Answer

Exactly!

anonymous · Answer

oh haha thanks!:)

callisto · Answer

You're welcome!
I suggest you to do all the exercises of the chapter(s) related to polynomials, and past paper (10 years +) too. That should be enough for you to be familiarized with this topic.