The function given is,
[tex]f(x)=x^4+6x^3+173x^2+332x+164[/tex]To find the zeros of the function , set the function equals to zero.
[tex]x^4+6x^3+173x^2+332x+164=0.[/tex]We have to check for the integers for which function equals to zero.
[tex](-1)^4+6(-1)^3+173(-1)^2+332(-1)+164[/tex][tex]1-6+173-332+164[/tex][tex]338-338=0[/tex]For x equals to -1 , the given function is zero.
Therefore, the zero of the polynomial is ,
[tex]x=-1.[/tex]