Factor x3 + x2 + x + 1 over the complex numbers.

(x+1)(x+i)(x-i)

Step-by-step explanation:

x3 + x2 + x + 1

Group factor:  x2(x+1) + (x+1)

= (x+1)(x2 + 1) = (x+1)(x+i)(x-i)

geometry: triangles

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answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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