Question

What is the condition for `x^2+ax+b` to be divisible by x+c?

Answer 1

`c^2-ac+b=0`

Explanation:

If and only if a polynomial `f(x)` is divisible by `x-a`, we can factor `f(x)` to `f(x)=(x-a)g(x)`.
Substitute `x=a` and you will find `f(a)=0`! This is called factor theorem.

For this question, let `f(x)=x^2+ax+b`. When `f(x)` is divisible by `x+c`, `f(-c)=0` must be satisfied.

`f(-c)=0`
`(-c)^2+a*(-c)+b=0`
`c^2-ac+b=0`