29 .51 Expression $x^{2}-y^{2}-z^{2}+2 y z+x+y-z$
(A) has no linear factor with integer coefficients and integer exponents.
(B) has a factor $-x+y+z$.
(C) has a factor $x-y-z+1$.
(D) has a factor $x+y-z+1$.
(E) has a factor $x-y+z+1$.
(14th American High School Mathematics Examination, 1963)
[Solution]
$$
\begin{aligned}
\text { Original expression } & =x^{2}-\left(y^{2}-2 y z+z^{2}\right)+x+y-z \\
& =x^{2}-(y-z)^{2}+x+y-z \\
& =(x+y-z)(x-y+z)+(x+y-z) \\
& =(x+y-z)(x-y+z+1) .
\end{aligned}
$$

Therefore, the correct choice is $(E)$.