There are a number of factors that can be said to have divided Americans in the 1980s. If your instructor wants one specific answer, you should probably look in your book or your notes because answers to this could vary. I will discuss three things that we can cite as factors that divided Americans at this time.
One factor was the Vietnam War. The war ended for the US in 1973, but its legacy was still with us in the 1980s. The memory of Vietnam helped to create divides between Americans who wanted a stronger foreign policy (and more patriotism in general) and those who wanted a more modest foreign policy (and a less aggressive form of patriotism). This could be seen, for example, in the different reactions to the Contras in Nicaragua. Republicans wanted to help the Contras fight communism while Democrats felt that American money should not go to support rebels in relatively unimportant countries.
Another factor was race. Racial issues left over from the Civil Rights Era split Americans during the 1980s. Problems of race played out in issues such as affirmative action and welfare. Affirmative action programs had come about in the 1970s as a way to make up for past discrimination against African Americans. Welfare was connected to the “Great Society” programs of the Johnson administration in the 1960s. By the 1980s, both of these issues (along with the issue of crime) were hot button topics among conservatives. Conservatives wanted to do away with affirmative action and to be tougher on crime and stingier on welfare. All of these issues were important to the candidacy of Ronald Reagan and of George H.W. Bush. Reagan denounced “welfare queens” and Bush ran a menacing picture of the African American murderer Willie Horton. Democrats saw these things as attempts to pander to racial animosity. In these ways, Americans were split by issues that were tied to race.
Finally, Americans were divided by the “culture wars.” These were conflicts over social issues such as abortion, gender roles, and homosexuality and by issues such as how patriotism was to be defined. Conservatives who held to conventional values were feeling that those values were under attack in modern America. They felt that American culture was losing its respect for men and that women were being encouraged to step outside of their traditional roles. They felt that abortion (which had been legalized in the 1970s) was immoral. They were generally anti-gay and uninterested in doing much to try to help people with AIDS (which came to prominence in the mid-80s). They were upset over a Supreme Court decision legalizing the burning of the American flag and by people who were unhappy about the phrase “under God” in the Pledge of Allegiance. Liberals took the opposite side on most of these issues.
All of these were factors that divided Americans in the 1980s. There is no objective way to say which one of them is the most important factor. You should check with your book or your instructor to find out which answer you are expected to give.