x3 + x2 + 4x + 4 = (x2 + 4)(x + 1)
x4 - 1.We can not "solve" this as we have not been told the value of x. However, we can simplify this expression:We have an x and a minus x here which will cancel out. Likewise the x2 and x3 will cancel out with the -x2 and -x3 respectively. This therefore leaves us with just x4 - 1.
x3 + x2 - 6x + 4 = (x - 1)(x2 + 2x - 4)
x3 - x2 + x - 2 has no rational factors.
3 - 3x + x2 - x3 = (1 - x)(x2 + 3)
x3 + x2 - 3x - 3 x(x2 + x - 3) - 3
x3 - x2 + 2x = x*(x2 - x + 2) which cannot be factored further.
x2 + x3
x2(x3 + 1) is the best you can do there.
(xn+2-1)/(x2-1)
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)