Find the linear factors of `x^(2)-5xy+4y^(2)+x+2y-2`

Explanation

Given expression is
`x^(2)-5xy+4y^(2)x+2y-2`………………I
Its corresponding equation is
`x^(2)-5xy+4y^(2)+x+2y-2=0`
or `x^(2)-x(5y-1)+4y^(2)+2y-2=0`
`:.x=((5y-1)+-sqrt((5y-1)^(2)-4.1.(4y^(2)+2y-2)))/2`
`=((5y-1)+-sqrt((9y^(2)-18y+9))/2`
`=((5y-1)+-sqrt((3y-3)^(2))/2`
`=((5y-1)+-(3y-3))/2=4y-2,y+1`
`:.` The required linear factors are `(x-4y+z)` and `(x-y-1)`.