Brandon Jennings is either a shot-happy, injury-plagued point guard who hasn’t lost his ego but has lost his explosiveness and won’t work well in Phil Jackson’s triangle. Or he’s a student of the game’s history, ready for a bust-out season and return to dynamic form — far enough removed from his 2015 Achilles tendon injury to be a steal on a one-year, $5 million Knicks contract at age 26.

The opinions vary dramatically on Jennings, who in perhaps a bad omen will wear No. 3 — Stephon Marbury’s former number.

The Post has learned Jennings requested a one-year contract to give himself a chance to prove himself and boost his stock for 2017’s free-agent bonanza. The Knicks were obliging as they seek to keep open 2017 cap space.

His rehab over, Jennings didn’t make his debut last season for Detroit until Dec. 29 versus the Knicks, was traded to Orlando Feb. 17 and didn’t excel in either place.

“It’s hard to have a judgment on his three-and-a-half months back,” said one NBA source who has spoken to Jennings. “There’s usually a one-year lag time on Achilles injuries. We’ll see this year and people will see he’s healthy again. He wasn’t going to get value on a long-term deal. He didn’t have his lateral quickness back.”

Sources have indicated it was Jennings who asked for a trade from Detroit — not thrilled to be in a backup situation with Reggie Jackson the Pistons’ No. 1 guy for the future. Jennings wanted a chance to prove himself to another organization before free agency, but the move to join his former Bucks coach Scott Skiles in Orlando turned into a nightmare. He shot 36.6 percent and Skiles didn’t enjoy the reunion.

“He likes him as a person, but on the court this season he couldn’t stand him because of his shot selection,’’ one person connected to the Magic told The Post. “When he got there, he just wanted to play street ball, one-on-one stuff.”

Skiles eventually quit after the season because of philosophical differences with management regarding talent, according to sources. But a person connected to the former Magic coach insisted “he wasn’t against the Jennings trade.”

There were still skeptics at the Orlando summer league who wonder if the Knicks’ point-guard situation could turn into a mess. According to NBA sources, the Knicks were interested in Jennings because he has the ability to fill in as a starter in case something goes wrong with Derrick Rose’s knees.

“Between the two of them, maybe you’ll get 82 games,” one cynical scout quipped.

Another NBA scout had limited enthusiasm about the signing.

“I think it isn’t a bad low-risk gamble on a one-year deal, but I’m not a big fan,” the scout said. “If he’s healthy, he can score. But he didn’t look right last year. Another year will likely help. He could be a nice, low-cost signing, but his history doesn’t inspire me.”

According to a source, Jackson and Jennings, who is from Compton, Calif., and works out in the offseason at UCLA, spoke for the first time by Skype on Sunday for an hour. Jackson was in Orlando and the two have never met.

On Monday, the sides agreed to terms. Jackson discussed with Jennings the triangle offense that Jeff Hornacek will still use, though they expect Jennings to excel in the new coach’s edict of picking up the pace.

Whether Jennings quickly grasps the triangle’s nuances is a big issue, but the Knicks believe he’s a lot better passer than he’s given credit for.

“The Brandon Jennings we saw last winter wasn’t the same Brandon Jennings we saw years ago,” one NBA general manager said. “He wasn’t anywhere near that rock ‘n’ roller. He knows how to get his shot off. He likes to shoot. The problem was he wasn’t making many. Orlando was his proving ground. It’s worth a gamble and he’ll like the spotlight of New York, have more confidence in his leg and start from scratch with a training camp.”

One individual close to Jennings calls him “a free spirit.” Detroit brass regarded Jennings as an extremely hard worker who loves the game and its history. That gives him perhaps a stronger chance of getting back to close to what he once was — when he averaged at least 15 points and five assists in his first six seasons.

Jennings, who has the same trainer as Rose, also is something of a savant.

“Ask him any trivia question about basketball, he’ll get it right,” said one individual who worked with Jennings in Detroit. “And he loves to play, loves the game, loves its history. He knows all about all the old players. Ask him a score of an important playoff game from the 1980s, he’ll know it.”

Another person who has a relationship with Jennings said: “He likes the big stage, he’s not afraid of having more attention.”

One former associate of Jennings said he’ll enjoy the New York media.

“He’s a really good talker with a high opinion of himself,” the person said.