“He knows sometimes you’ve got to make those throws, you can’t be worried about losing a job,” Redskins tight end Fred Davis says of quarterback Rex Grossman, above. (Pablo Martinez Monsivais/Associated Press)

When Rex Grossman was handed a clipboard and banished to the sideline last month, the Washington Redskins dropped three straight games and saw their playoff chances disappear. Grossman was asked Wednesday if he wonders how the team’s fortunes might be different had Coach Mike Shanahan stuck with him at quarterback rather than hand the job to John Beck last month.

“Yeah,” Grossman said, “but why would I answer that?”

Left unsaid around Redskins Park for much of the past month is that there are stark differences between Grossman and Beck. While some were on display in last weekend’s loss at Miami, where Grossman regained his starting job but failed to lead the team to a touchdown, teammates hope they’re more evident against the Dallas Cowboys Sundays, when the Redskins try to end their five-game losing streak.

While Beck struggled in his three starts, coaches and players hope Grossman’s experience and confidence will help spark an offense that has scored just one touchdown in the past three games. Despite his high interception rate, players say Grossman isn’t hesitant to take shots downfield, something Beck didn’t seem willing to do during his stint as starter.

“He knows sometimes you’ve got to make those throws, you can’t be worried about losing a job,” tight end Fred Davis said when asked about the differences between Grossman and Beck. “You just have to go out there and play, do your best . . . you give it your best effort, you’ll see what happens, and the guys around you will make plays for you.”

Following Beck’s final start, Nov. 6 against San Francisco, some players expressed frustration that the quarterback didn’t look their way downfield. Grossman has shown the ability to involve a variety of wide receivers and tight ends in the offense. Beck, meanwhile, targeted running back Roy Helu 16 times against the 49ers. He aimed at his top wide receiver, Jabar Gaffney, only five times that game.

The differences between the two quarterbacks were evident early against the Dolphins. By the end of the first quarter, Grossman had completed a 17-yard pass to Leonard Hankerson and a 20-yarder to Gaffney. The previous week, Beck had no completions downfield, and his longest completion of the day was a deflected short pass that happened to land in his running back’s arms.

“He finds people down the field,” left tackle Trent Williams said of Grossman. “He moves the ball. When Rex is in there, the ball is moving down the field. We have our nicks in the red zone where we step on our own foot; other than that, he does a great job.”

Against Miami, Grossman had seven completions of 16 yards or more, including four that topped 18. In Beck’s starts against San Francisco and Buffalo, he totaled six completions for 16 yards or more, and only three for at least 18.

In his nine starts in a Redskins jersey, Grossman has shown that he takes more chances downfield. His return to the huddle could mean the game plan against the Cowboys includes more deep routes for receivers.

“I guess the law of averages are, the more chances you take downfield, the more you’re going to get big plays,” said wide receiver Anthony Armstrong, who has only one catch since Week 2. The longest of Armstrong’s five catches this season is a 15-yarder. A year ago, Armstrong averaged 19.8 yards per reception and had seven catches of at least 45 yards.

After watching the offense inch forward the past few weeks, Redskins pass catchers say all they want is an opportunity to make a big play.

“He’s going to take chances to throw it up there and give you the chance to go up and get it,” Davis said of Grossman. “And whenever you have that opportunity, it’s a good thing."

Before Shanahan handed the job to Beck last month, some of Grossman’s teammates spoke up, saying Grossman deserved another chance despite throwing four interceptions against Philadelphia on Oct. 16. Grossman said he was disappointed by the demotion but tried to make the most of his time on the bench.

“You have a month or so to reset yourself and what your goals are,” he said, “and what you need to get accomplished and how to go about it.”

When Grossman lost his job, the Redskins’ offense looked strikingly different. Tim Hightower was still in the mix. Kory Lichtensteiger and Chris Cooley were starting. Santana Moss and Jammal Brown were healthy and in the lineup. And Niles Paul was often the first wide receiver off the bench. This week, as injuries continue to pile up, it’s not clear which players the Redskins will start at right tackle, left guard, wide receiver or running back.

“It’s always going to look a little bit different when you do have injuries,” Grossman said.

Grossman raised some eyebrows with his preseason pronouncement that the Redskins would win the division title. The Redskins now sit at 3-6, and while the quarterback says he is still optimistic, he also realizes Washington needs to change its fortunes this weekend.

“Nobody’s given up. Everybody believes that we should be a lot better than we are,” he said.

In last weekend’s 20-9 loss, Grossman was 21-of-32 passing for 215 yards. He had two interceptions and a passer rating of 58.7, but perhaps most noticeably, failed to get the Redskins into the end zone.

“Anytime you don’t win, there’s always a couple plays that could’ve made the difference,” Grossman said. “You can’t really pat yourself on the back too much. For the most part, I did what I was coached to do and made a lot of plays. But not enough.”

Staff writer Mike Jones contributed to this report