Question

x^3+2x^2-5x-6怎么分解呢？ 还有x^3-7x+6

详细的过程写出来

Answer 1

X3+2x2-5x-6
= X3+2x2+x-6(x+1)
=x(x+1)2-6(x+1)
=(x+1)(x2+x-6)
=(x+1)(x+3)(x-2)

X3-7x+6
=x3-x2+x2-7x+6
=x2(x-1)+(x-6)(x-1)
=(x-1)(x2+x-6)
=(x-1)(x+3)(x-2)
这类题型就属于添项凑项法类型的题目，其中还穿插着十字相乘法，希望对你有用

Answer 2

x³+2x²-5x-6=0
x(x²+2x+1)-6x-6=0
x(x+1)²-6(x+1)=0
(x+1)(x²+x-6)=0
(x+1)(x-2)(x+3)=0

x³-7x+6=0
x³+x²-6x-x²-x+6=0
(x³+x²-6x)-(x²+x-6)=0
x(x²+x-6)-(x²+x-6)=0
(x-1)(x²+x-6)=0
(x-1)(x-2)(x+3)=0