Question

what belief united the progressive movement? that societys problems could be solved, that education needed reform, that political bosses should not hold office, that there should be a federal income ta

Answer 1

That society's problems could be solved.

Progressives were united by the belief that social and political problems created by industrialization and urbanization could be fixed through reform, science, expertise, and active government intervention (rather than by leaving things to laissez-faire or machine politics). The other choices were specific goals within the movement (education reform, fighting political bosses, supporting an income tax), but the overarching unifying belief was that problems were solvable.