对任意整数n,多项式(4n+5)²-9都能被 A:被8n整除 B:被n整除 C:被2n+1整除 D:被8(n-1)整除到底选哪个呀
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 11:40:45
![对任意整数n,多项式(4n+5)²-9都能被 A:被8n整除 B:被n整除 C:被2n+1整除 D:被8(n-1)整除到底选哪个呀](/uploads/image/z/1602240-24-0.jpg?t=%E5%AF%B9%E4%BB%BB%E6%84%8F%E6%95%B4%E6%95%B0n%2C%E5%A4%9A%E9%A1%B9%E5%BC%8F%EF%BC%884n%2B5%EF%BC%89%26%23178%3B-9%E9%83%BD%E8%83%BD%E8%A2%AB+A%EF%BC%9A%E8%A2%AB8n%E6%95%B4%E9%99%A4+B%EF%BC%9A%E8%A2%ABn%E6%95%B4%E9%99%A4+C%EF%BC%9A%E8%A2%AB2n%2B1%E6%95%B4%E9%99%A4+D%3A%E8%A2%AB8%28n-1%29%E6%95%B4%E9%99%A4%E5%88%B0%E5%BA%95%E9%80%89%E5%93%AA%E4%B8%AA%E5%91%80)
对任意整数n,多项式(4n+5)²-9都能被 A:被8n整除 B:被n整除 C:被2n+1整除 D:被8(n-1)整除到底选哪个呀
对任意整数n,多项式(4n+5)²-9都能被 A:被8n整除 B:被n整除 C:被2n+1整除 D:被8(n-1)整除
到底选哪个呀
对任意整数n,多项式(4n+5)²-9都能被 A:被8n整除 B:被n整除 C:被2n+1整除 D:被8(n-1)整除到底选哪个呀
选C,原式可化成4(2n+1)(2n+4) ,写错了
(4n+5)^2-9
=(4n+5-3)(4n+5+3)
=(4n+2)(4n+8)
=8(2n+1)(n+2)
C:被2n+1整除