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?
That's clever. My answer was long division. Took me a second to figure out your way. Is that something you were taught, or did you come up with it on the spot?
Comments
1/975 + 1/1053 = 1/3 (1/325 + 1/351) = 1/3 676/325/351 = oh, this one looks not very beautiful
The other one is equally beautiful. Try factoring more.