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Set values of m

Source: 1964 AHSME Problem 25

August 23, 2013
algebrapolynomialconicsparameterizationAMC

Problem Statement

The set of values of mm for which x2+3xy+x+my−mx^2+3xy+x+my-m has two factors, with integer coefficients, which are linear in xx and yy, is precisely:
<spanclass=′latex−bold′>(A)</span> 0,12,−12<spanclass=′latex−bold′>(B)</span> 0,12<spanclass=′latex−bold′>(C)</span> 12,−12<spanclass=′latex−bold′>(D)</span> 12<spanclass=′latex−bold′>(E)</span> 0 <span class='latex-bold'>(A)</span>\ 0, 12, -12\qquad<span class='latex-bold'>(B)</span>\ 0, 12\qquad<span class='latex-bold'>(C)</span>\ 12, -12\qquad<span class='latex-bold'>(D)</span>\ 12\qquad<span class='latex-bold'>(E)</span>\ 0
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