That expression can't actually be factored without using complex numbers. If you want to use complex numbers, then it would come out as a "difference of squares":
(x + i)(x - i)
It is: x squared -1 = (x-1)(x+1) when factorized
x2 + x2 + x2 = (1 + 1 + 1)x2 = 3x2
x2+8x+12 = 0 When factorized: (x+6)(x+2) = 0 Therefore: x = -6 or x = -2
x2+10x+21 = (x+3)(x+7) when factored.....
x4 +x2 =x2 (x2+1)
x3 + x2 + 4x + 4 = (x2 + 4)(x + 1)
If you mean t^2 +11t +10 then it is (t+10)(t+1) when factorized
The factors of x2 are x and x x times x plus 1 = x2 + x
(xn+2-1)/(x2-1)ExplanationLet Y=1+x2+x4+...+xn. Now notice that:Y=1+x2+x4+...+xn=x2(1+x2+x4+...+xn-2)+1Y+xn+2=x2(1+x2+x4+...+xn-2+xn)+1Y+xn+2=x2*Y+1Y+xn+2-x2*Y=1Y-x2*Y=1-xn+2Y(1-x2)=1-xn+2Y=(1-xn+2)/(1-x2)=(xn+2-1)/(x2-1)
(x2 - x + 1)(x2 + x + 1)
(xn+2-1)/(x2-1)
x2(x3 + 1) is the best you can do there.