Polynomial inequalities and sign charts

Polynomial inequalities and sign charts

Solve polynomial inequalities by factoring, locating real zeros and tracking signs on the resulting intervals. This precalculus practice emphasizes the reasoning behind a sign chart, including the different effects of odd and even root multiplicities.

Tasks include cubic and quartic inequalities, strict and nonstrict comparisons, isolated equality solutions, a factored sign table and a model restricted to a finite input interval. Error analysis examines why dividing by a variable factor can lose or introduce solutions.

Prerequisites are factoring, real roots, multiplicity, interval notation and basic inequality logic. Single-select and multiselect questions move from sign interpretation to transformations, parameter conditions and contextual decisions. Each question supplies its own data and does not depend on a previous answer.

Record the zeros, test signs and check endpoints in the original inequality before selecting a response. Detailed explanations justify each included interval and distinguish a zero from a positive or negative value. Work without a calculator unless checking your own sketch. The set supports independent solution methods, while a selected answer alone does not establish that the complete sign argument has been mastered.