Working with Jay Gruden, right, has Kirk Cousins on the verge of a third straight season with 4,000 yards passing. (Mark Tenally/AP)

Washington’s front office will spend the final month of the season analyzing whether the team should try to retain its high-priced quarterback. The answer could determine coach Jay Gruden’s future, too.

If Kirk Cousins shows the Redskins what they’re looking for and agrees to a long-term deal, then there’s no reason to get rid of Gruden, who signed a three-year extension through 2020 before the season began. Gruden has had a fruitful relationship with Cousins, who’s on the verge of his third straight 4,000-yard passing season.

But if Cousins and a team decimated by injuries stumbles to the finish line, a chain of events may lead to owner Dan Snyder falling back on a penchant for canning coaches.

The Redskins (5-7) finish with a soft schedule with home games against the Cardinals and Broncos sandwiched between visits to the Chargers and Giants.

Repeats of the lackluster effort the team gave in a 38-14 loss to Dallas would reflect poorly on the coach and quarterback, maybe poorly enough to convince the impatient owner to let Cousins leave in free agency and send Gruden packing.

Snyder needs to decide what he wants to do quickly. The Giants’ search for a coach has already started. Picking one requires fast action. If Snyder stalls, his team will be left with few options like it was in 2008, when a month-long search resulted in the disastrous promotion of offensive coordinator Jim Zorn. He went 12-20 over two seasons.

If the Redskins fire Gruden, a new staff needs to be in place in time to evaluate quarterbacks at the NFL Combine in February. The team must decide by March 14 whether to tag Cousins a third time for $34.5 million or simply cut ties.

It’s really a joint decision. If the Redskins are willing to shell out for another year of quarterback continuity, it wouldn’t make sense to get rid of Gruden and force Cousins to learn a new coach’s system. And Gruden’s ability to coax the most out of Cousins is the best case for keeping the coach.

Gruden can’t assume all the blame for a 5-7 record. A promising start created hope for a 10-win season before injuries depleted talent on both sides of the ball. Gruden’s four-year mark of 26-33-1 looks ugly, but the players are behind him, and he’s played his hand well. He should be the first coach under Snyder to reach a fifth season.

Washington should try to keep Cousins after the best three-year stretch ever by a Redskins passer. Even after losing two 1,000-yard receivers in the offseason, Cousins has found a way to produce with lackluster replacements.

Still, the bottom line is that the Redskins are almost certainly going to miss the playoffs for a second straight year.

Now the final four games could very well decide if the Gruden-Cousins era continues.

Read more columns from Rick Snider:

These Redskins are still trying to prove their worth for next year

The Redskins’ run game has been shoddy. It’s time to give up on it.

The Redskins’ defense has historically employed mercenaries. This year it has leaders.

While Redskins fill up the training room, their season is heading to the morgue