Find the linear factors of `2x^2-y^2-x+x y+2y-1.`

Explanation

Given expression is
`2x^(2) - y^(2) - x + xy + 2y -1` (1)
Its corresponding equation is
`2x^(2) - y^(2) - x +xy + 2y - 1 = 0`
or `2x^(2)-(1 -y)x - (y^(2) - 2y + 1) = 0`
`therefore x = (1-y pm sqrt((1-y)^(2) + 4.2(y^(2)-2y + 1)))/(4)`
`= (1-y pm sqrt((1-y)^(2) + 8(y-1)^(2)))/(4)`
`= (1-y pm sqrt(9(1-y^(2))))/(4)`
`= (1-y pm 3(1-y))/(4)`
`1 - y, - (1 -y)/(2)`
Hence, the required factors are (x + y -1) and (2x - y + 1).