Recently, I was solving a school problem for my niece: what are the values of a and b in ax^8 - bx^7 + 1 = 0 to make it divisable by (1 - x)^2? Children in Taiwan are taught to do it by long division, but me, I started with writing a(x^4 - 1)^2 - bx(x^3 - 1)^2 + ... and 1st qst was, why do u do it?