6n^3+9n^2+n-1怎么因式分解为什么你们会想到拆掉9n^2,还有利用2n-1

观察它等于0的一个解为-1/2
则有一个因式为n+1/2
6n^3+9n^2+n-1=(6n^2+6n-2)(n+1/2)=2(n+1/2)(3n^2+3n-1)

6n^3+9n^2+n-1
=6n^3+3n^2+6n^2+n-1
=(2n+1)·3n^2+ 6n^2+n-1+2n-2n
=(2n+1)·3n^2+3n(2n+1)-1-2n
=(2n+1)·3n^2+3n(2n+1)-(1+2n)
=(2n+1)·(3n^2+3n-1)

6n³+9n²+n-1
=(2n+1)·3n² + (2n+1)·3n - (2n+1)
(分组分解）
=(2n+1)(3n²+3n-1)
（有理数范围的话,到这里就结束了）
=3·(2n+1)（x+1/2+√21/6)(x+1/2-√21/6)
（实数范围,利用求根公式）

6n³+9n²+n-1
=(2n+1)·3n² + (2n+1)·3n - (2n+1)
=(2n+1)(3n²+3n-1)