Question

【题目】多项式(x+yz)(xy+z)(y+zx)(zxy)的公因式是( )

A. x+yzB. xy+zC. y+zxD. 不存在

Answer 1

【答案】A

【解析】

(x+y-z)(x-y+z)-(y+z-x)(z-x-y)

=(x+y-z)(x-y+z)+(y+z-x)(x+y-z)

=(x+y-z)(x-y+z+y+z-x)

=2z(x+y-z)

故多项式(x+yz)(xy+z)(y+zx)(zxy)的公因式是：x+yz.

故选：A.