Eli Manning takes off during the first half. The Giants quarterback threw three touchdown passes and no interceptions Sunday night. (Kathy Willens/ASSOCIATED PRESS)

The self-education continued for another NFC East team, now into its 12th week.

The New York Giants walloped the Green Bay Packers, 38-10, at MetLife Stadium on Sunday night, and it was interesting enough to watch the defending Super Bowl champion dismantle the champ from two seasons ago. But the Giants, like the Washington Redskins, maintained their longstanding ability to confuse their fans and keep the league from knowing how good, exactly, this team truly is.

These Giants didn’t look battered or unsure of themselves, as they did in two previous losses. They looked elite. If nothing else, New York’s seventh victory prevented a head-to-head battle against the Redskins next weekend at FedEx Field for first place in the NFC East. But that was about all Sunday’s win accomplished, at least for the long term.

“This gives us a little breathing room,” Giants quarterback Eli Manning said. “But not much.”

Otherwise, the questions about Manning’s arm strength and health were quieted, if not answered. The worries about a defense that, entering Sunday, had slipped to 23rd in the league by allowing 371.6 yards per game were eased but not eliminated.

Games like this one, and the one the Redskins won last Thursday against the Dallas Cowboys, have made this season so interesting — and no easier to understand. On Sunday, the Giants sacked Packers quarterback Aaron Rodgers five times and continually forced last year’s most valuable player to scramble and eventually throw passes away. Where was that pressure throughout this the season?

More important, where had this Manning been? He threw three touchdown passes Sunday, but before that his most recent scoring throw came five weeks earlier against the Redskins. Manning’s slump led to concerns that his arm must not be healthy; the phrase “tired arm” became a common whisper in the New York area. And although Manning and Coach Tom Coughlin denied anything out of the ordinary, the quarterback disappeared to Mississippi during the Giants’ bye week and put himself on a football moratorium. No film study, no planning discussions and certainly no throwing.

These are issues, among others, that Redskins fans could surely understand, if not exactly empathize with. Three weeks ago, Washington Coach Mike Shanahan publicly wondered if his team, at the time 3-6, shouldn’t just go ahead and begin looking toward 2013. He quickly backtracked from those comments, but with a loss to the hapless Carolina Panthers, a defense depleted by injuries, and a rookie quarterback, Robert Griffin III, reflecting on two average games, Shanahan wasn’t the only one looking toward the future.

The season seemed to be in real trouble for both teams, and the bye week was a welcome break for each. When they returned, Washington outscored its next two opponents 69-37 in a pair of wins, and the Giants (7-4) snapped a two-game losing streak Sunday by dominating the Packers (7-4).

Maybe these recent flashes are nothing more than post-bye fool’s gold. The teams are rested, and adjustments have been made.

Since 2008, Manning hasn’t lost a game immediately after a bye. But can a few days in Mississippi really recharge the mind, body and soul the way it appeared to do for Manning on Sunday?

“You didn’t realize you were tired until you see how quickly we were moving,” Manning said of watching his team practice after a week off. “There was a different enthusiasm for practice this past week.”

Whatever the case, he looked rejuvenated, and others noticed.

“Tonight was one of those games where he was alive, and he was making some of those plays, and he was distributing the ball the way we’re used to,” said wide receiver Victor Cruz, who caught Manning’s second touchdown throw of the night.

Manning’s passes weren’t always perfect — he overthrew fullback Henry Hynoski in the end zone in the first quarter and later badly underthrew Hakeem Nicks — but he adjusted. Manning made a 25-yard pass to Nicks in the second quarter look easy, and he found Rueben Randle in the back of the end zone for his first scoring pass.

Whatever was suspected of being wrong with Manning was, for one night, hidden beneath a 249-yard passing performance. These were similar to the concerns that, midway through Griffin’s rookie season, defenses had already begun learning how to stop the youngster.

On Sunday, New York’s defense showed no intimidation against Rodgers. The Giants’ defensive line has made itself famous, but their secondary frustrated the Green Bay quarterback as much as anything. New York’s defensive backs closed passing windows, and while Rodgers searched for an opening or ran toward one, there was that defensive line, latching onto him again. Other than a six-sack performance against San Francisco in the season’s sixth week, Sunday was the Packers’ season-high.

“To have him throw the ball on our timing, rather than his, we were glad to see that,” Giants Coach Tom Coughlin said of Rodgers.

This is the fun part of the NFL, but it’s also the most maddening. Who is a contender, and who will be exposed in due time?

The Giants are used to this, having entered the final turn of two mediocre seasons, 2007 and ’11, on a hot streak — then ended them each time by lifting the Super Bowl trophy.

Was it rest during those seasons? Or just adjustments? Maybe it just takes time for a team to find itself.

No, next week’s game, between two teams searching for identity, won’t be for first place in the division. But it’ll go a long way toward validating or casting doubt on what has been seen in these recent weeks.