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Provo • Blowout wins over the Pac-12's Oregon State and the bottom tier of the Western Athletic Conference — Idaho, New Mexico State and Hawaii — just didn't do it. And neither did close wins over a pair of midlevel WAC teams — San Jose State and Utah State — or a season-opening conquest of a Southeastern Conference team, Ole Miss.

The BYU Cougars are still searching for a signature win to validate their 2011 football season, but they are running out of time. The last chance comes Friday in the Armed Forces Bowl (11 a.m., ESPN) against an 8-4 Tulsa team that could make a case for being the second-best club the Cougars will have faced this season.

The 9-3 Cougars have defeated only one team that finished the regular season with a winning record (USU), and are looking at the bowl as an opportunity to not only get to the 10-win plateau, but also something to hang their hat on when critics charge Bronco Mendenhall's 2011 iteration couldn't win the big one.

"Man, you just want to finish off the season right," said quarterback Riley Nelson, the team's emotional leader. "On the line I guess is just the validation of our preparation, because we have worked really hard to get to a bowl game. Then once you are in a bowl game, you don't want to lose just because it leaves a bad taste in your mouth all through winter."

And sullies your reputation.

Mendenhall touched on that notion last week, relating a story of how he asked his players if they watched Temple rout Wyoming in the New Mexico Bowl the previous Saturday, and how most of them who viewed it had an unfavorable impression of the Cowboys.

"They formed their impressions of those programs by just one game at the end," Mendenhall said.

Which is why some of the Cougars are acknowledging that Friday's nationally televised game gives them the chance to finally feel good about what they accomplished — if they beat a Tulsa team whose only losses were to teams ranked in the top 10 at the time: Oklahoma, Oklahoma State, Boise State and Houston.

"I think what most people don't understand about a football team is that you are with these guys every day, for hours," said backup QB James Lark. "And they become your best friends, practically your family. The last thing we would want would be for our seniors to go out with a loss, and us not playing the way we are capable of playing.

"So pretty much it is for each other," Lark continued. "We want to go out and finish it right, and we want to win. There is never a time when we don't want to win."

It's just that a win Friday would seem like two or three, given the weakness of the latter half of the Cougars' schedule. And even Mendenhall admitted that there's something magical about a 10-win season, as opposed to nine or fewer.

Having already recorded four seasons of 10 or more wins in his seven-year tenure, Mendenhall can join Oklahoma's Bob Stoops and Georgia's Mark Richt as the only coaches with five 10-win seasons in their first seven seasons.

"I think [10 wins] is a big difference when you talk about credibility and you talk about programs," Mendenhall said. "Ten is difficult and I think any coach you ask, or anyone that follows sports, if there is a 10-win team consistently, they are one of the best in the country."

drew@sltrib.comTwitter: @drewjay