Question

For what value of m the expression $y^2+4xy+4x+my-2$ can be resolved into two rational factors-

• A. 1
• B. -1
• C. 2
• D. -2

Answer 1

The correct option is B -1

condition for $a{x}^2+2hxy+b{y}^2+2gx+2fy+c$

$abc+2fgh-a{f}^2-b{g}^2-c{h}^2=0$

$a=0,h=2,b=1,g=2,f=\frac{m}{2},c=-2$

$2\times \frac{m}{2}\times 2\times 2=-1\times 4+2\times 4=0$

$4m-4+8=0$

$4m+4=0$

$m=\frac{-4}{4}$

$m=-1$