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# What is a polynomial function for 5, i, -i?

##f(x)=x^3-5x^2+x-5##

I have assumed that ##{5,i,-i}## are intended to be the of the function.

In this case, the function can be factored as: ##color(white)("XXX")(x-5)((x-i)(x+i)##

##color(white)("XXX")=(x-5)(x^2-i^2)##

##color(white)("XXX")=(x-5)(x^2+1)##

##color(white)("XXX")=x^3+x -5x^x-5##

(or in standard polynomial form) ##color(white)("XXX")=x^3-5x^2+x-5##