Question

if (y+1) and (y+2) are factors of the polynomial y3+3y2-3py+q,find p and q

Answer 1

Put y=-1, get an expression in p and q
Put y=-2, get another expression in p and q.

solve the two equations.

y+1 is a factor means y+1=0

Answer 2

y=-1,-2
-1+3+3p+q=0 (1) where y =-1
-8+12+6p+q =0 (2) where y=-2
3p+q=-2
6p+q=-4
substact both sides
-3p=2
p=-2/3
and q=0