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In this interactive pre-calculus lesson, students learn how to sketch a fifth-degree polynomial step by step. Using factoring, synthetic division, the factor theorem, and end behavior, they discover how to find roots, identify intercepts, and build the graph. Trial and error becomes a powerful tool as students test possible roots and confirm factors. By the end, learners understand how to connect algebraic solutions with the visual shape of the polynomial, setting the stage for more advanced graphing techniques in calculus.
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