experiment
(8x-3)(x+1), middle term is 5x, nope
(8x+3)(x-1), middle term is -5x, nope
(8x-1)(x+3), middle term is 23x, nope
(8x+1)(x-3), middle term is -23x,nope
(2x-3)(4x+1), middle term is -10x,nope
(2x+3)(4x-1), middle term is 10x, nope
(2x+1)(4x-3). milddle term is -2x, nope
(2x-1)(4x+3), middle term is 2x, YES
(2x-1)(4x+3)