x3+27y3 = (x+3y) · (x2-3xy+9y2)
(x + 2)(x^2+4)
x3 + 8 = x3 + 23 = (x + 2)(x2 + 2x + 22) = (x + 2)(x2 + 2x + 4)
(x + 5)(x^2 + 2x + 2)
(x + 2)(x^2 + 2x + 3)
x3 + x2 + 4x + 4 = (x2 + 4)(x + 1)
x3 + 4x2 + x + 4 = (x + 4)(x2 + 1)
x3+27y3 = (x+3y) · (x2-3xy+9y2)
x2(x3 + 1) is the best you can do there.
x(x^2 + 2)
(x + 2)(x^2+4)
(x + 1)(x2 - x + 1)
(x2 - xy + y2)(x + y)
x3 + 8 = x3 + 23 = (x + 2)[x2 - (x)(2) + 22] = (x + 2) (x2 - 2x + 4)
x3 + 8 = x3 + 23 = (x + 2)(x2 + 2x + 22) = (x + 2)(x2 + 2x + 4)
x3 - 3x2 + x - 3 = (x2 +1)( x - 3)
x3 - 2x2 + x - 2 =(x - 2)(x2 + 1)