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

1 Answer
Jan 20, 2018

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