Resposta:

P(x)=ax³+bx²+cx+d

P(1)=a+b+c+d =0 (i)

x+1=0 ==>x=-1

P(-1)=-a+b-c+d=6  (ii)

x-2=0 ==> x=2

P(2)=8a+4b+2c+d=6 (iii)

x+2=0 ==>x=-2

P(-2)=-8a+4b-4c+d=6 (iv)

a+b+c+d =0   (i)

-a+b-c+d=6  (ii)

8a+4b+2c+d=6 (iii)

-8a+4b-4c+d=6  (iv)

(i)+(ii)

2b+2d=6 ==>b+d=3  ==> d=3-b (v)

(iii)+(iv)

8b+2d=12 ==>4b+d=6 (vi)

(v)  em (vi)

4b+3-b = 6  ==> 3b=3 ==>b=1

usando (v)  ==> d=3-1 =2

Manipulando 8a+4b+2c+d=6 (iii)

Fazendo b=1 e d=2 , temos:

8a+4+2c+2=6 ==> 8a+2c=0  ==>c=-4a  (vii)

Usando -a+b-c+d=6  (ii)  , Fazendo b=1 e d=2  e c=-4a , temos:

-a+1+4a+2=6  ==>3a=3  ==>a=1   e c=-4a=-4

P(x)=x³+x²-4x+2  é a resposta