The polynomial p(x,y,z)= 2x2+6y2+3z2+7xy+11yz+7xz
by setting z=0:
p(x,y,0)=2x2+6y2+7xy=(2x+3y)(x+2y)
and next setting y=0:
p(x,0,z)= 2x2+3z2+7xz
=(2x+z)(x+3z)
By comparing the obtained factorizations and
completing each factor with the additional terms from the
other factorization, we obtain the factorization of
P(x, y, z)=(2x+3y+z)(x+2y+3z)
Also, notice that on substituting x = 0, we
obtain
P (0, y, z) =6y2+3z2+11yz=(3y+z)(2y+3z),
in accordance with the factorization
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