Question 732873
The function polynomial in expanded form is {{{x^4+0*x^3-10x^2+0*x+9}}}.


Testing for -9 and +9 will fail, giving nonzero remainders.


Test for -3:
1___0___-10___0___9
___-3___9____3___-9
---------------------------------
1___-3___-1___3____0
ROOT.


Test for +3:
1___-3___-1___3
____3___0___-3
-------------------------
1___0___-1___0
ROOT.


I won't even check for -1 and +1, since I see from the corresponding quotient from the last test, {{{x^2-1}}} is difference of two squares, {{{(x-1)(x+1)}}}.  Roots are +1 and -1.


Roots found are -3, +3, -1, +1.