for (x+1) and (x+2) be a factor of given polynomialp(x) , they must be its roots. and

hence according to remainder theorem p(-1) and p(-2) must be 0,

so p(-1)=-1-a+b-8=0

p(-2)=-8-4a+2b-8=0

solving these 2 simentanous equation.

b-a=9

b-2a=8

so b= 10 and a is 1

and polynomial becomes x^3-x^2-10x-8=0

since product of roots is 8(-d/a) and 2 roots are -1 and -2 last root must be 4 so factor is (x-4)

you could also go for long division.!!!

cheers