Problem: The set of values of for which has two factors, with integer coefficients, which are linear in and , is precisely:
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let the linear factors be and . When multiplied out and equated to the given expression, we obtain these equations between the coefficients: (1) (2) (3) (4) (5) .
From equations (1) and (5), either or . With the first set of values equation (3), becomes . Substituting into equation (4), we have . If . If and . The second set of values, , yields the same results because of the symmetry of the equations.