Albert Barnes Commentary Jeremiah 3:8

"And I saw, when, for this very cause that backsliding Israel had committed adultery, I had put her away and given her a bill of divorcement, yet treacherous Judah her sister feared not; but she also went and played the harlot." — Jeremiah 3:8 (ASV)

Rather, And I saw that because apostate Israel had committed adultery, I had put her away, and given her the writing of her divorcement, yet false Judah her sister feared not... The expression, For all the causes whereby, is probably the actual formula with which writings of divorcement commenced.