f[x_]:=x^2-2x+2
Plot[f[x],{x,-2,4},PlotLabel->"#14, p. 230"]
(* No real roots: *)
Solve[f[x]==0,x]
Factor[f[x],Extension->{Sqrt[2],I}]

f[x_]:=x^2+2x-1
Plot[f[x],{x,-3,3},PlotLabel->"#23, p. 230"]
Solve[f[x]==0,x]
Factor[f[x],Extension->{Sqrt[2],I}]

f[x_]:=3-4x-4x^2;
Plot[f[x],{x,-3,3},PlotLabel->"#32, p. 230"]
Solve[f[x]==0,x]
Factor[f[x],Extension->{Sqrt[2],I}]