Question

find the values of 'm'for which xsq.+3xy+x+my-m has two linear factors in x and y with integer coefficients

Answer 1

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Answer 2

Let x^2 +3xy+x+my- m=(ax+by+c)(ex+fy+g)

Since the given expression does not contain y^2 then 1 of the linear factor must contain the term y

Therefore x^2 +3xy+x+my-m
=(ax+by+c)(ex+g)or ; x^2 +3xy+x+my -
m=aex^2 +bexy+cex+agx+bgy+cg .

Equating the coefficients from both side
ae=1 _____ 1
be=3 _____2
ce+ag=1____3
bg=m_____4
cg=-m_____5

From 1
a=e=1

Therefore from 2
b=3

putting in 3
c+g=1___6

Now dividing 4 by 5
b÷c =1

Therefore 6
3+g=1
g = 4

putting in 5
-m = -3 ×4
m = 12

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