let the polynomial be

p(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants

if x1=1, x2=1+sqt.2 and x3=1-sqt.2 are the roots of p(x), then p(x) can be written in the form

p(x) = a (x - x1)(x - x2)(x - x3)

p(x) = a (x - 1)(x - 1 - sqt.2)(x - 1 + sqt.2)

p (x) = a(x-1)(x^2 - 2x + 1 - 2) = a(x-1)(x^2 - 2x - 1) = a(x^3 - 3x^2 + x + 1)

we also know that

for x = 2

p(2) = -2 that is

a(2^3 - 3*2^2 + 2 + 1) = -2

a(8 - 12 + 3) = - 2

a = - 2/ (-1)

a = 2

thus the polynomial is

p(x) = 2(x^3 - 3x^2 + x + 1)

p(x) = 2x^3 - 6x^2 + 2x + 2.