Answer :

For the given 2 degree equation


That must be equal to(ax + by + c)(dx + e)


= ad.x2 + bd.xy + cd.x + ea.x + be.y + ec


= ad.x2 + bd.xy + (cd + ea).x + be.y + ec


x2 + 3xy + x + my–m = ad.x2 + bd.xy + (cd + ea).x + be.y + ec


compare the equation


and take out the coefficient of every term


a.d = 1 ----------1


b.d = 3 ----------2


c.d + e.a = 1 ----------3


b.e = m ----------4


e.c = -m ----------5


from eq 1; a = d = 1 all coefficient are integers


After putting result in eq 3; c + e = 1 -------6


After putting result in eq 2; b = 3 --------7


divide eq 4 and 5




that implies b = -c = -3 eq 7


Put value of c in eq 6


-3 + e = 1


e = 1 + 3 = 4


Putting value of b and e in eq 4


m = b × e


m = 3 × 4 = 12


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