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Provo • Potential, progress and improvement.

Trying the patience of his school's fan base at times, BYU football coach Bronco Mendenhall has used those words to describe his team this year, almost from the time the Cougars were inexplicably humiliated 31-16 by Utah State to drop their record to 1-4.

After BYU walloped Colorado State 49-10 in Fort Collins on Saturday and started looking ahead to this week's final home game, against 1-9 New Mexico, Mendenhall began to allow that some "significant" strides have been made. BYU is now 5-5, and can become eligible for a bowl game with one win in its next two games.

"We took another step forward in our execution as a football team," said Mendenhall, who withheld judgment in that regard after the Cougars crushed UNLV on Nov. 6, saying in so many words that the Rebels (2-8) did not provide a true test.

"We have two more opportunities in the regular season, and I don't think we've reached our potential yet, and there's an urgency that I feel and I think our team feels to reach that potential," he said.

The most significant progress lately has been made by the offense, especially on third down.

The Cougars were 12-for-13 on third-down conversions against the Rams (3-8), and the only time they didn't convert, they were just a half-yard short, and picked that up on fourth down.

It was the first time they have had a third-down conversion rate above 80 percent since a 12-for-14 performance against Washington in 2008. BYU entered the game converting at 42 percent, and is now at 45 percent, 26th-best in the country.

The Cougars led the country in that category two of the past three years.

"That's how you have to play great football," said quarterback Jake Heaps, now 4-3 as a starter. "You have to convert on third downs. That's a huge part of the game. When you convert on third down it builds a lot of momentum for your offense and tears down the defense. For us to be able to do that consistently and put drives together, and convert in tough situations, it just kind of shows how our offense is clicking right now."

Mendenhall said the key was getting into third-and-short situations. The longest third-down situation Heaps was asked to convert was third-and-9 (twice).

Mendenhall said neither he nor offensive coordinator Robert Anae saw the near-perfect game on offense coming.

"Hard to predict when certain parts of the team are going to emerge and in what situations," he said. "We have been diligently working away at it, and it has just been coming on their own schedule. That was good to see today."

The Cougars have moved up to No. 83 in the country in total offense, and No. 89 in scoring offense.

"We had the momentum building. This just happened at the right time for us. We have been working hard. We know what we are capable of. It is just a matter of going out and doing it," Heaps said, when asked if he was surprised by the lopsided win. "This isn't a shock to me. We could have been doing this since Week 1, so it has taken us a little while to get there."

drew@sltrib.comTwitter: @drewjay —

Saturday's Game

P New Mexico (1-9) at BYU (5-5), 4 p.m.

TV • Versus —

BYU's third-down conversions: last 3 games

Date Opponent On Third Down

Oct. 23 Wyoming 5 of 13

Nov. 6 UNLV 11 of 17

Nov. 13 Colorado State 12 of 13