Do police officers “routinely lie to serve their own interests?” Thirty-one percent of Americans believe they do, and that number rises to 45 percent among African-Americans, 41 percent among young people and 39 percent among Democrats. Republicans reject that charge three to one (60 to 20 percent).

Those numbers come from a national poll of Americans just conducted by Reuters and the Ipsos polling organization. (Explore the full results here.) Still, the image of the police is more controversial than the reality.

Asked whether they approve of the job being done by “your local police department,” nearly three quarters of Americans say they approve. Approval is high among African-Americans (56 percent) as well as whites (77 percent), among Democrats (72 percent) as well as Republicans (84 percent).

On the other hand, the public is divided over whether “Police officers tend to unfairly target minorities” (37 percent agree, 43 percent disagree). African-Americans and Latinos believe the police do target minorities (69 percent and 54 percent, respectively). Fewer than a third of whites feel that way (29 percent).

The racist image of the police is strongly influenced by politics. A majority of Democrats (53 percent) believe the police unfairly target minorities. Only 19 percent of Republicans agree.

Young people don’t trust the police. That’s not surprising. They’re the ones most likely to get into trouble. In the Reuters poll, young people were more than twice as likely as seniors to endorse the view that police officers tend to unfairly target minorities (53 percent among Americans under 30, 25 percent among those 60 and older).

These days, young Americans are much more likely than seniors to live in a multicultural world and to interact with minorities. Even young whites were more than twice as likely as white seniors to brand the police as racist (42 percent of young whites but only 20 percent of white seniors).

Do Americans “trust the police to be fair and just?” Most do (53 percent). But that, too, is a political issue. Only 30 percent of African-Americans, 43 percent of young people and 47 percent of Democrats say they trust the police to be fair and just. Trust in the police is much higher among seniors (67 percent) and Republicans (70 percent).

Overall, these findings are reminiscent of research showing that Americans tend to be highly critical of Congress, while they hold a favorable view of “your own congressman.” That’s why they regularly re-elect over 90 percent of congressional incumbents even while denouncing the institution.Education researchers have found that college students tend to give low marks when asked to assess the quality of teaching in their schools. However, when asked to rate the quality of the teacher in the most recent class they attended, the marks come out much higher.

The same rule appears to apply to people’s view of the police: “The police may tend to be unfair and racist, but police officers around here are O.K.”

The poll also asked people whether they have a favorable impression of the Ferguson police department. Very few Americans have any experience with the Ferguson police department. They probably didn’t even know Ferguson was a town in Missouri a year ago. Only 21,000 people live there, out of 316 million Americans. What the public knows about the Ferguson police is what they see on television and read in the news.

And that is intensely political — and racial. Sixty-two percent of Americans say they have a favorable impression of the Ferguson police. But there’s a huge difference between African-Americans (32 percent favorable) and whites (69 percent). Republicans are overwhelmingly favorable to the Ferguson police (85 percent). Democrats are divided (51 percent favorable, 49 percent unfavorable).

One question was surprisingly less divisive: “Would you approve of your children (or future children) becoming police officers?” Americans as a whole say yes, 59 to 22 percent. Young people? 68 percent yes. Democrats? 58 percent yes. African-Americans? More tentative, but still favorable. By 45 to 30 percent, blacks approve of their children becoming police officers. In this case, reality — “It’s a good job” — is more positive than image.

PHOTO: A protester yells at a line of police officers during a demonstration against the grand jury decision in the Ferguson, Missouri shooting of Michael Brown in San Francisco, California, Nov. 28, 2014. REUTERS/Elijah Nouvelage