Federal agents have fanned out across Austin to try to stop a serial bomber, a race against time and technology that again puts the FBI under a public microscope.

More than 300 federal agents have been assigned to the case. Such high-profile, fast-moving investigations tend to generate what FBI agents call “shotgun leads” — scattershot tips sending investigators in many directions, most leading nowhere. But any one could help solve the case.

“In a big case like this, you have to be nimble, and you have to not close out any leads prematurely,” said Rick DesLauriers, a former FBI official who in 2013 led the hunt for the Boston Marathon bombers. FBI profilers, evidence specialists and bomb experts are scouring evidence for clues that might point them to a suspect or a group of suspects.

“No federal expense or resource is being spared,” DesLauriers said, noting that the Boston case was broken by video evidence showing the bombers.

In recent months, the FBI has made headlines for all manner of controversies. It is an agency under regular public attack from President Trump as it investigates some of his associates and whether anyone helped Russia interfere with the 2016 election. The bureau has also come under sharp criticism from elected officials for failing to act on a warning that a Florida teenager might try shooting up a school — a tip that came just weeks before Nikolas Cruz allegedly killed 17 people in Parkland.

Now, the FBI faces pressure to stop a bomber who has shown a remarkable capacity to build bombs. Two people have been killed by the homemade explosives.

On Tuesday, after a bomb exploded overnight at a FedEx package sorting facility in San Antonio, officials said they had found an undamaged package sent by the same person. Officials declined to say whether that package contained an unexploded bomb.

“With serial bombings, a lot of the work is forensics — how much of the bomb you have, how much of a signature is there to its construction, the type of material, etc.,’’ said David Gomez, a former FBI supervisor. When agents recover an exploded bomb, they painstakingly search for fingerprints or DNA evidence, then try to rebuild it to determine all the components and see whether it points to a particular store or purchaser. With an unexploded device, all that potential evidence is at hand.

For instance, in the 2011 case of a homemade bomb left along the route of a Martin Luther King Jr. Day parade in Spokane, Wash., agents found that the bombmaker used fishing weights as shrapnel. To make the bomb more dangerous, the bombmaker coated the weights in a chemical common in rat poison that inhibits blood coagulation.

The bomb never detonated. FBI agents traced the weights to a particular fishing supply store, where they found a debit card receipt that led them to Kevin Harpham, who received a ­32-year prison sentence for his attempted attack.

Investigators also focus on creating a geographic profile for the Austin bomber, Gomez said.

“The first crime tends to happen in what is their comfort area, some place they are familiar with, and the very first victim may be targeted rather than random,” he said.

In the case of a serial arsonist couple who torched dozens of abandoned structures on the Eastern Shore of Virginia in 2012 and 2013, a geographic profile based on their early targets pointed to the street where the couple lived.

As local and federal authorities search for the Austin bomber, there are some details that perplex explosives experts. The bomber’s quickly changing methods, frequent attacks and lack of demands stand out to current and former law enforcement officials.

Ted Kaczynski, known as the Unabomber, took more than three years to carry out his first five attacks. The Austin bomber carried out the same number in less than three weeks.

“It’s very unusual that someone will do this many at one time,” said Malcolm Brady, a retired explosives investigator with the Bureau of Alcohol, Tobacco, Firearms and Explosives. “Whatever his motivation is, it’s significant and severe. You don’t normally get this compressed of a schedule.”

Brady, who investigated the 1993 bombing of the World Trade Center in New York City, said he was intrigued that the bomb that injured two people on Sunday used a tripwire as a triggering device.

“A tripwire is highly, highly unusual,” he said. “To me, that raises a question about whether he has a military background or is just reading about that stuff online.”

Mary Ellen O’Toole, a former FBI profiler now at George Mason University, said the frenetic pace of the attacks could help investigators catch the bomber.

“When you see a serial offender increase their activity, he’s bound to make mistakes — and in his case a mistake could cost him fingers, it could kill him, or he could just become sloppy because he’s so excited about what he’s doing,” she said. “The motivation has probably evolved over the last two weeks. Now he’s probably enjoying all of the attention and the feeling of ­omnipotence he has creating so much concern and fear.”