The splitting field of x2 − 1 over F7 is F7 since x2 − 1 = (x + 1)(x − 1) already splits into linear factors.
the spLITtING fieLd Of x2 − 1 OVEr f7 iS F7 SInce x2 − 1 = (x + 1)(X − 1) alreAdY splits INTO LINEar fActoRS.