The greatest common factor of 1-x3 is 1, dummy.
x5-1 = (x - 1)(x4 + x3 + x2 + 1)
x3+x2+x First, factor out the x: x(x2+x+1) Could stop there, but the rest is factor-able using imaginary numbers: x(x+.5(1+i(3).5)(x+.5(1-i(3).5), where i = (-1).5, or sqrt(-1)
(x + 1)(x - 2)(x + 5)
x3 + 9x2 + 27x + 27 Given the numbers in the equation, we can likely bet on (x + 3) being a factor. Let's try it with artificial division: 3 * 1 = 3 9 - 3 = 6 3 * 6 = 18 27 - 18 = 9 3 * 9 = 27 27 - 27 = 0 Bingo. So let's carry it out in long division:                       x2 + 6x + 9                    _____________________ x + 3 ) x3 + 9x2 + 27x + 27                        x3 + 3x2                                        6x2 + 27x                                        6x2 + 18x                                                                9x + 27                                                                9x + 27                                                                                    0 So we have: x3 + 9x2 + 27x + 27 = (x + 3)(x2 + 6x + 9) Which we can now factor further with relative ease: = (x + 3)(x + 3)(x + 3) = (x + 3)3
The greatest common factor of 1-x3 is 1, dummy.
(x + 1)(x2 - x + 1)
(x - 1)(x2 + x - 1)
x3 + 2x2 + 5x + 4 = (x + 1)(x2 + x + 4)
x2(x3 + 1) is the best you can do there.
x3 - 3x2 + x - 3 = (x2 +1)( x - 3)
x3 - 2x2 + x - 2 =(x - 2)(x2 + 1)
x3 - 3x2 + x - 3 = (x - 3)(x2 + 1)
3 - 3x + x2 - x3 = (1 - x)(x2 + 3)
x3 + 1 = x3 + x2 - x2 - x + x + 1 = x2(x + 1) - x(x + 1) +1(x + 1) = (x + 1)(x2 - x + 1)
x3 + x2 + 4x + 4 = (x2 + 4)(x + 1)
x3 + 4x2 + x + 4 = (x + 4)(x2 + 1)