What is the quotation (x^3-3x^2 +3x-2)÷(x^2-x+1)

(x^3 - 3·x^2 + 3·x - 2) / (x^2 - x + 1)

= (x - 2)·(x^2 - x + 1) / (x^2 - x + 1)

= x - 2

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4