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#