用三种方法分解公因式：a的四次方＋a的三次方＋a+1

题目

用三种方法分解公因式：a的四次方＋a的三次方＋a+1

答案

a⁴＋a³＋a+1
=a³(a+1)+(a+1)
=(a+1)(a³+1)
=(a+1)(a+1)(a²-a+1)
=(a+1)²(a²-a+1)
a⁴＋a³＋a+1
=(a⁴+a)+(a³+1)
=a(a³+1)+(a³+1)
=(a+1)(a³+1)
下面与法1相同
a⁴＋a³＋a+1
=a⁴-2a²+1+(a³+2a²+a)
=(a²-1)²+a(a²+2a+1)
=(a+1)²(a-1)²+a(a+1)²
=(a+1)²[(a-1)²+a]
=(a+1)²(a²-a+1)