Please do now and explain

Please do now and explain For what value of 'a' of the polynomial x3 + 2x2y + axy2 + 2y3 divisible by x + y

if f(x) is divisible by x+y thus per factor theorem f(-y)=0
f(x) = x³ +2x²y +axy² +2y³ 
f(-y) = (-y)³ +2(-y)²y +a(-y)y² +2y³  = 0
=- y³ +2y³ - ay³ +2y³   = 0
= - ay³ +3y³ = 0
ay³  = +3y³  
thus a= 3