Question 974211
a(x^3+x^2+x+d)=0

factors are inverses of roots
(x+2)(x+1)(x-4)
Multiply them:
first two are x^2+3x+2
multiply by (x-4)
x^3-4x^2+3x^2-12x+2x-8
=x^3-x^2-10x-8, the general form of the polynomial

a(x^3-x^2-10x-8)=2, when x=1

a(1-1-10-8)=2
-18a=2
a=-1/9

polynomial is (-1/9)(x^3-x^2-10x-8)




{{{graph(300,300,-10,10,-10,10,(-1/9)(x^3-x^2-10x-8))}}}