Throughout Wednesday's debate, Democratic nominee for governor Jay Gonzalez and Republican Gov. Charlie Baker traded jabs about some of the critical issues facing Massachusetts, and in one case faced an unanticipated question involving partisan politics.

WGBH News offers some context and fact-checking for many of the claims at the heart of the divisions between Baker and Gonzalez.

Gov. Baker backs Trump-supporting U.S. Senate candidate Geoff Diehl.

"One more question for him. Governor, are you going to vote for Geoff Diehl?" - Jay Gonzalez

Yes. In the debate, Baker was asked directly if he'd vote for Diehl in November and the governor said he would decide later and let everyone know. That decision-making process lasted around 35 minutes, because Baker immediately declared that he would vote for Diehl once reporters asked him after the debate. Baker told the press that he'd misspoke and would vote for the entire GOP ticket.

Previously, Baker’s blessing was offered as blanket support for Republicans running statewide. In early September, Baker told reporters he “endorsed the ticket,” which includes Diehl who is looking to unseat incumbent Sen. Elizabeth Warren. Diehl is widely known for helping lead Trump’s state campaign in Massachusetts. Baker has repeatedly noted that he did not vote for either Trump or his Democratic opponent, Hillary Clinton, in 2016.

Republican Attorney General hopeful, Jay McMahon is also a Trump supporter.

Asked last month if he would commit to attending a Diehl fundraiser, Baker didn’t answer directly and instead suggested he’d be more focused on his own race and campaigning for Republicans candidates for state office, according to the State House News Service.

It took 19 months for the Baker administration to hire an outside auditor to investigate the State Police's payroll fraud scandal.

"People who are indicted. People who pled guilty, criminal activity during the governor's tenure. And the first incident of this was reported 19 months ago and they're just hiring someone to come in and look at payroll and personnel practices?" - Jay Gonzalez

WCVB began reporting that state troopers were skipping shifts and abusing the overtime payroll system in the fall of 2017. As the scandal expanded, the head of the agency was replaced by Col. Kerry Gilpin, who lead an internal investigation that has resulted in numerous state and federal charges against troopers.

In April of this year, Gilpin announced plans to hire an independent auditor to conduct an outside review of the State Police's payroll system, seven months after the scandal broke. In September, over 12 months after the news initially broke, Gilpin hired Ernst and Young to perform the audit.

Gonzalez's claim that it took Baker 19 months to perform the audit is based on the April 2017 suspension of Trooper Eric Chin for payroll fraud.

Baker has a plan to fix the MBTA's maintenance backlog.

"Yes, we definitely need to invest more, and we have a plan to do that." - Gov. Charlie Baker

There's the start of a plan. Since so much of the T's "capital investment plan" through 2023 is going to service expansion and improvement, only 56 percent of the $8 billion touted by Baker at the debate can be considered as going to "fix" the MBTA's over $7 billion "state of good repair" backlog of things that need to be repaired or replaced. That leaves around $3.5 billion of work without a firm plan in place.

MassDOT and the MBTA sets capital spending — investment in large one-time projects over several years — in five-year plans. The current five-year plan began in July 2018 and includes the $8 billion Baker mentioned to be spent on repairs and replacements, like new buses, signal systems and winter resiliency work, as well as expansion projects like the Green Line extension to Medford.

The $8 billion also includes payments toward the new Red and Orange Line vehicles expected to begin service next year.

Problems at the MBTA took center stage soon after Baker entered office in 2015. Baker and the Legislature established a new fiscal governing board for the agency and launched a two-pronged strategy: short-term operational spending cuts and cost controls to balance the T's budget, teamed with long-term investment of capital dollars back into the system.

Gonzalez's debate claim that Baker expects the T to take 15 years to repair is based on the Baker team's early estimate that it would take that amount of time to repair the entire MBTA maintenance backlog.

Under Baker, the state's gas utility lines are being monitored safely.

"I believe the focus should be on investing and upgrading and modernizing and improving the quality of the existing infrastructure." - Gov. Charlie Baker

The federal Department of Transportation visited Massachusetts this past summer and gave the state's Department of Public Utilities gas line inspection program a nearly perfect score. The fed's one caveat: Only two of the state's eight inspectors were on active duty in the field and the investigators thought the state should do more to bring up their numbers. Still, the same report praised DPU for the frequency of their inspections.

DPU inspectors completed 1,066 inspections in 2017, up from 880 in 2016 and 822 in 2015. The number of inspectors on state payroll has fluctuated between eight and 12, according to the governor's office. At the time of the federal evaluation, only two of the eight were available because of management positions, medical disability and training.

Gonzalez, Baker spar over education funding and closing the achievement gap.

“I think we have a lot of work left to do on education…" - Gov. Charlie Baker

"Governor Baker has been governor for four years now and made no progress on the fact that we have some of the biggest achievement gaps in the country, and funding disparities for public schools are growing even bigger." - Jay Gonzalez

Here’s a topic both sides take issue with. Though Baker argues that his administration increased Chapter 70 funding, designated for school spending, critics argue that pace does not keep up with growing needs throughout the Commonwealth.

This year, both the House and Senate attempted to rectify this issue with an overhaul of the school funding formula, but ultimately couldn't reconcile the legislation. Meanwhile, some school districts, lead by Brockton, are weighing a lawsuit against the state over flagging school funding.

Nevertheless, the administration has touted that since taking office four years ago Baker has increased school spending by $507 million, boosting investments in the latest budget to $4.91 billion. Baker claims through those investments, his administration has made good on recommendations most education advocates agree would improve the school funding formula.

When in charge of the state budget, Gonzalez cut funding for early childhood education by 14.5 percent.

"When he was the ANF secretary, he cut it by $85 million while he was raising state spending by 6.5 billion." - Gov. Charlie Baker

The state spent $585,736 on early childhood education in fiscal year 2009, the last budget before the Great Recession forced massive cuts and cratered state spending. That funding bottomed out in the fiscal 2013 budget at just under $500,000 and recovered to $500,378 in fiscal 2014, the last budget contributed to by Gonzalez before he left the Patrick administration. That represents a decrease of 14.57 percent between fiscal 2009 and 2014, or around $85 million.

Gonzalez's campaign admits that "as Secretary, Jay had to make deep cuts to close the gap," during the budget troubles of the late aughts.

Baker's claim that overall state spending went up by $6.5 billion over the same time period is appears to be off, controlling for a number of factors. Adjusted for inflation, the fiscal year 2014 budget was $3.57 billion more than the 2009 budget. (The state approved $28.1 billion of spending in fiscal year 2009 and that number rose to $34 billion by the end of Gonzalez's time managing the budget in fiscal 2014, an increase of around $5.9 billion not counting for inflation.)

Gonzalez has a plan to raise taxes. Baker does not.

“It’s a very specific plan to raise $3 billion each year, by the end of my first term, which is $3 billion more than zero, which is his plan.” - Jay Gonzalez

"The notion that he has put enough plans on the table to fund all the stuff he's promising and committing to simply isn't true." - Gov. Charlie Baker.

True. Jay Gonzalez plan to raise $3 billion in new revenue would rely on levying taxes on the wealthiest Massachusetts residents and endowments of the state’s top colleges and universities.

Three billion dollars might sound like a lot, but MassGOP has attacked Gonzalez’s proposal as falling woefully short of funding his full agenda which they claim tops $60 billion dollars. Among other Gonzalez agenda items, the Republican’s price tag includes costs to fund single-payer health care, universal pre-k and the North-South Rail Link.

Gonzalez has rejected this assessment.

That additional revenue, Gonzalez says, would then be spent on shoring up the state’s aging transportation infrastructure and boosting K-12 schools throughout the state.

Despite its popularity, a proposed constitutional amendment that would tax those making more than $1 million to generate an estimated $2 billion in new revenue, failed to pass constitutional muster because of how it was written. Gonzalez has said he wishes to revive the so-called millionaire's tax as governor. He also wishes to tax university endowments exceeding $1 billion in order to fund spending on education and transportation. Both revenue-raising proposals would need to go through a rigorous legislative process.

Backed by the tax-averse House, Baker has only raised taxes in a few limited situations and has approached the issue on a case-by-case basis.