作业帮分解因式 x的立方-3x²+4 x³+6x²+11x+6 x³+5x²+3x-9题目上不小心打到一起去了。x的立方-3x²+4 x³+6x²+11x+6x³+5x²+3x-9
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/09 07:35:39
分解因式 x的立方-3x²+4 x³+6x²+11x+6 x³+5x²+3x-9题目上不小心打到一起去了。x的立方-3x²+4 x³+6x²+11x+6x³+5x²+3x-9
分解因式 x的立方-3x²+4 x³+6x²+11x+6 x³+5x²+3x-9
题目上不小心打到一起去了。
x的立方-3x²+4
x³+6x²+11x+6
x³+5x²+3x-9
分解因式 x的立方-3x²+4 x³+6x²+11x+6 x³+5x²+3x-9题目上不小心打到一起去了。x的立方-3x²+4 x³+6x²+11x+6x³+5x²+3x-9
x³-3x²+4
=x²(x-3)-(x-3)+x+1
=(x-3)(x+1)(x-1)+(x+1)
=(x+1)(x²-4x+4)
=(x+1)(x-2)^2
x³+6x²+11x+6
=x²(x+6)-(x+6)+12x+12
=(x+6)(x+1)(x-1)+12(x+1)
=(x+1)(x²+5x-6+12)
=(x+1)(x+2)(x+3)
x³+5x²+3x-9
=x²(x+5)-(x+5)+4x-4
=(x+5)(x+1)(x-1)+4(x-1)
=(x-1)(x²+6x+5+4)
=(x-1)(x+3)^2
x^3 - 3x^2 + 4
=(x^3 + 1) - (3x^2 - 3)
=(x+1)(x^2 - x + 1) - 3(x+1)(x-1)
=(x+1)[(x^2 - x + 1) - 3(x-1)]
=(x+1)(x^2 - 4x + 4)
=(x+1)(x-2)^2
x^3 + 6x^2 + 11x + 6
=(x^3 + 1)+(...
全部展开
x^3 - 3x^2 + 4
=(x^3 + 1) - (3x^2 - 3)
=(x+1)(x^2 - x + 1) - 3(x+1)(x-1)
=(x+1)[(x^2 - x + 1) - 3(x-1)]
=(x+1)(x^2 - 4x + 4)
=(x+1)(x-2)^2
x^3 + 6x^2 + 11x + 6
=(x^3 + 1)+(6x^2 + 11x + 5)
=(x+1)(x^2 - x + 1) + (x+1)(6x+5)
=(x+1)[(x^2 - x + 1) + (6x+5)]
=(x+1)(x^2 + 5x + 6)
=(x+1)(x+2)(x+3)
x^3 + 5x^2 + 3x - 9
=(x^3 - 1) + (5x^2 + 3x - 8)
=(x-1)(x^2 + x + 1) + (x-1)(5x+8)
=(x-1)[(x^2 + x + 1) + (5x+8)]
=(x-1)(x^2 + 6x + 9)
=(x-1)(x+3)^2
收起