计算四阶行列式D4=|x111||1x11||11x1||111x|

计算四阶行列式D₄=
|x111|
|1x11|
|11x1|
|111x|
【正确答案】：D₄= |x+3 x+3 x+3 x+3| | 1 x 1 1 | | 1 1 x 1 | | 1 1 1 x | =(x+3) |1 1 1 1| |1 x 1 1| |1 1 x 1| |1 1 1 x| =(x+3) |1 1 1 1| |0 x-1 0 0| |0 0 x-1 0| |0 0 0 x-1| =(x+3)(x-1)³．