Group the terms like so,
[tex]x^3-4x^2+7x-28=(x^3-4x^2)+(7x-28)[/tex]
The first group has terms with a common factor of [tex]x^2[/tex], and the second has a common factor of 7:
[tex]x^2(x-4)+7(x-4)[/tex]
Now both terms have a common factor of [tex]x-4[/tex]:
[tex](x^2+7)(x-4)[/tex]
