tag:blogger.com,1999:blog-2400513859305780710.post250127735038669879..comments2023-04-04T07:53:53.789-07:00Comments on Mathematical Food For Thought: Polynomial Power. Topic: Algebra/Polynomials. Level: AIME.Jeffrey Wanghttp://www.blogger.com/profile/11114458640271201663noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-2400513859305780710.post-77907967922602962722005-11-21T19:02:33.000-08:002005-11-21T19:02:33.000-08:00#1. x^4 + 64 = x^4 + 16x^2 - 16x^2 + 64= (x^2 + 8...#1. x^4 + 64 = x^4 + 16x^2 - 16x^2 + 64<br>= (x^2 + 8 )^2 - (4x)^2<br>= (x^2 + 4x + 8 ) (x^2 - 4x + 8 )<br><br>Took me awhile to realize there were no monomial factors =P<br><br>#2. P(x) = (x - 1)(x - 2)(x - 3)...(x - n) + x<br>P(n+1) = n! + n + 1QCnoreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-70743351215551802462005-11-21T19:34:05.000-08:002005-11-21T19:34:05.000-08:00Why are you making weird faces? =P Anyway, your an...Why are you making weird faces? =P Anyway, your answers are correct; I should post harder problems.paladin8noreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-43109876097404545362005-11-22T19:56:27.000-08:002005-11-22T19:56:27.000-08:00dang slick solution to #14 hahadang slick solution to #14 hahagotztahbeaznnoreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-47252783463955267282005-11-24T16:54:28.000-08:002005-11-24T16:54:28.000-08:001. \( x^4+64 = (x^2+8)^2-2x^2(8)=(x^2+8)^2-(4x)^2=...1. \( x^4+64 = (x^2+8)^2-2x^2(8)=(x^2+8)^2-(4x)^2=(x^2+4x+8)(x^2-4x+8).\)chess64http://www.upal.ca/adeelnoreply@blogger.com