Hillary Clinton has taken a 10-point lead over Donald Trump in a head-to-head match-up, extending her advantage by 4 points from a month ago, according to a national poll conducted after the Democratic National Convention.

Mrs. Clinton and her running mate, Virginia Gov. Tim Kaine, had a 10-point, 49 percent to 39 percent lead over Mr. Trump and GOP vice presidential nominee Mike Pence, according to the Fox News poll released Wednesday.

In a three-way match-up, Mrs. Clinton and Mr. Kaine were at 44 percent, the Trump-Pence ticket was at 35 percent, and the Libertarian Party ticket of former New Mexico Gov. Gary Johnson and former Massachusetts Gov. Bill Weld was at 12 percent.

In a Fox poll taken in late June, Mrs. Clinton had led Mr. Trump by 6 points head-to-head, 44 percent to 38 percent.

In a three-way match-up, Mrs. Clinton had been at 41 percent, Mr. Trump had been at 36 percent, and Mr. Johnson, the Libertarian Party’s presidential nominee, had been at 10 percent.

The new survey was taken Sunday through Tuesday. Analysts have said a better picture of the race is likely to develop in a few weeks, after effects from any post-convention bounces for Mrs. Clinton and Mr. Trump have settled.

In the new poll, 65 percent said Mrs. Clinton is at least somewhat qualified to be president, while 58 percent said Mr. Trump is “not very” or “not at all” qualified.

Sixty-four percent also said Mrs. Clinton has the temperament to serve effectively as president, while 61 percent said Mr. Trump does not.

Seventy-two percent said Mrs. Clinton has the knowledge to effectively serve as president, while 59 percent said Mr. Trump does not.

The two candidates, however, had almost identical ratings on honesty and trustworthiness. Thirty-six percent said Mrs. Clinton is honest and trustworthy, while 61 percent said she is not. Mr. Trump had a similar 36 percent/62 percent split.

Majorities of voters trusted Mrs. Clinton over Mr. Trump on the issues of climate change, race relations, education, drug addiction, foreign policy, health care, and immigration.

The candidates were tied at 47 percent apiece on terrorism and national security after a majority had sided with Mr. Trump on handling “terrorism” in May, although a majority did say they trust Mr. Trump more on “destroying terrorist groups like ISIS” in the new poll.

Majorities also trusted Mrs. Clinton over Mr. Trump on making decisions about using nuclear weapons, looking out for you and your family during tough economic times, and nominating the next Supreme Court justice.

A plurality, 49 percent to 42 percent, sided with Mrs. Clinton on “preserving and protecting the Constitution of the United States.”

Mr. Trump, meanwhile, had the edge on handling the federal deficit and the economy.

The candidates were tied at 43 percent apiece on “restoring trust in government.”

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