Answer:
True
Explanation:
Construct a second-degree polynomial q(x)=ex^2+fx+g
f(x)/(x+1) = q(x) + (2/(x+1))
= ((x+1) * q(x) + 2) / (x+1)
so f(x) = (x+1) * q(x) + 2
substitute our q(x):
f(x) = (x+1)(ex^2+fx+g) + 2
= ex^3 + fx^2 + gx + ex^2 + fx + g + 2
= ex^3 + (e+f)x^2 + (f+g)x + (g + 2)
this still equals ax^3+bx^2+cx+d so by like terms we have
e = a
e + f = b
f + g = c
g + 2 = d
This means we can find an infinite number of solutions that satisfy the property.