By the polynomial remainder theorem, a polynomial [tex]p(x)[/tex] has a factor of [tex]x-c[/tex] if [tex]p(c)=0[/tex]. So all you need to do is check the value of [tex]f(x)[/tex] at [tex]x=1,3,-3,5,-5[/tex]. You should get
[tex]f(1)=-96[/tex] (so [tex]x-1[/tex] is NOT a factor)
[tex]f(3)=-96[/tex] (so [tex]x-3[/tex] is NOT a factor)
[tex]f(-3)=f(5)=f(-5)=0[/tex] (so the last three options are factors)
