Problem: The expression x2−y2−z2+2yz+x+y−z has:
Answer Choices:
A. no linear factor with integer coefficients and integer exponents
B. the factor −x+y+z
C. the factor x−y−z+1
D. the factor x+y−z+1
E. the factor x−y+z+1
Solution:
x2−y2−z2+2yz+x+y−z=x2−(y2−2yz+z2)+x+y−z=x2−(y−z)2+x+y−z =(x+y−z)(x−y+z)+x+y−z=(x+y−z)(x−y+z+1)