x^2+2x+1 is a factor of ax^3+ax^2+bx+c then find a b c

Question

help!!

Answer 1

x^2+2x+1 is (x+1)^2

So, do a synthetic division twice by x+1 and you get remainders of

c-b and c-2b-a

Both those remainders must be zero, so
b=c and a+b=0

So, a can be anything, and b=c = -a and you have

ax^3 + ax^2 - ax - a
= a(x^3+x^2-x-1)
= a(x+1)^2 (x-1)