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Source: AHSME 1963 Problem 21

January 10, 2014
AMC

Problem Statement

The expression x2−y2−z2+2yz+x+y−zx^2-y^2-z^2+2yz+x+y-z has:
<spanclass=′latex−bold′>(A)</span> no linear factor with integer coeficients and integer exponents<span class='latex-bold'>(A)</span>\ \text{no linear factor with integer coeficients and integer exponents} \qquad
<spanclass=′latex−bold′>(B)</span> the factor −x+y+z <span class='latex-bold'>(B)</span>\ \text{the factor }-x+y+z \qquad
<spanclass=′latex−bold′>(C)</span> the factor x−y−z+1 <span class='latex-bold'>(C)</span>\ \text{the factor }x-y-z+1 \qquad
<spanclass=′latex−bold′>(D)</span> the factor x+y−z+1 <span class='latex-bold'>(D)</span>\ \text{the factor }x+y-z+1 \qquad
<spanclass=′latex−bold′>(E)</span> the factor x−y+z+1 <span class='latex-bold'>(E)</span>\ \text{the factor }x-y+z+1
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