x2 + x + 25 can not be factored.
x3 + x2 + 4x + 4 = (x2 + 4)(x + 1)
x2(x3 + 1) is the best you can do there.
x + 4
You can't factor it
That does not factor neatly.
x2 + 5x - 120 can not be factored.
x2 - 13 + 30 = x2 + 17, which has no real factors.