This math unit begins by introducing students to polynomial inequalities, starting with factored quadratic inequalities, where students analyze the sign of the polynomial over specified intervals and determine solution sets based on roots. The unit progresses to explore expanded quadratic expressions, increasing complexity by dealing with polynomials that include terms raised to various powers (multiplicity) and expanding to polynomials with up to three factors. Students practice determining the sign of these polynomials within intervals and identifying the ranges where polynomial expressions maintain a consistent sign to satisfy inequalities. Subsequently, the unit transitions to rational function inequalities, starting with simpler scenarios where a factored quadratic is divided by a binomial and steadily moving towards more complex rational expressions involving factors with multiplicities over binomial denominators. This segment enhances understanding of solving inequalities by evaluating signs over intervals and deducing solution sets with rational functions possessing various critical values and discontinuities. The entire progression culminates in a comprehensive grasp of polynomial roots, their impacts on inequalities, and deeper insights into algebraic functions and interval analysis.Skills you will learn include:
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