Question

问题补充：因式分解x的三次方减2x的二次方减7x减4 解方程 2x的三次方 36=11x的平方减3x

问题补充：因式分解x的三次方减2x的二次方减7x减4
解方程 2x的三次方+36=11x的平方减3x

Answer 1

个人觉得分解三次方程需要非常强的观察力，才能配出来
x³-2x²-7x-4=x³+x²-3x²-3x-4x-4
=x²(x+1)-3x(x+1)-4(x+1)
=(x²-3x-4)(x+1)
=(x+1)(x-4)(x+1)
=(x+1)²(x-4)

2x³+36=11x²-3x
2x³-11x²+3x+36=0
2x³-8x²-3x²+12x-9x+36=0
2x²(x-4)-3x(x-4)-9(x-4)=0
(2x²-3x-9)(x-4)=0
(2x+3)(x-3)(x-4)=0
x=-3/2, x=3, x=4

Answer 2

x³-2x²-7x-4
=x³+x²-3x²-3x-4x-4
=x²(x+1)-3x(x+1)-4(x+1)
=(x+1)(x²-3x-4)
=(x+1)(x+1)(x-4)
=(x+1)²(x-4)

2x³+36=11x²-3x
2x³-11x²+3x+36=0
2x³+3x²-14x²-21x²+24x+36=0
x²(2x+3)-7x(2x+3)+12(2x+3)=0
(2x+3)(x²-7x+12)=0
(2x+3)(x-2)(x-5)=0
x= -1.5，x= 2，x=5