Question

一道因式分解题，急

xyz+xy+yz+zx+x+y+z+1

Answer 1

原式=X(YZ+Y+Z)+(YZ+Y+Z+1)
=(X+1)(YZ+Y+Z+1)
=(X+1)(Y+1)(Z+1)

Answer 2

xyz+xy+yz+zx+x+y+z+1
=xyz+xy+yz+y+xz+x+z+1
=xy(z+1)+y(z+1)+x(z+1)+(z+1)
=(z+1)(xy+y+x+1)
=(z+1)(x+1)(y+1)

Answer 3

(xy+x+y+1)(z+1)或者（yz+y+z+1)(x+1)或者（xz+z+x+1)(y+1)

Answer 4

xyz+yz+zx+xy+x+y+z+1
=z(xy+y+x)+(xy+x+y)+(z+1)
=(xy+x+y)(z+1)+(z+1)
=(z+1)(xy+x+y+1)
=(z+1)[x(y+1)+(y+1)]
=(z+1)(x+1)(y+1)

Answer 5

(x+1)(y+1)(z+1)