Polynomial Functions

A complete set of lessons covering polynomial and quadratic tools — from factoring and graphing to solving, analyzing, and evaluating.

Learn to use the TI-84 to find polynomial maximums and minimums with clear examples, calculator guidance, and real-world optimization...

A complete set of lessons covering polynomial and quadratic tools — from factoring and graphing to solving, analyzing, and evaluating.

Use the Factor Theorem to test roots, identify factors quickly, and simplify polynomial expressions with confidence.

Solve higher-degree inequalities using graphs and sign analysis, then practice interval notation and sign changes with interactive problems.

Work backward from a graph to build its polynomial by analyzing intercepts, multiplicity, end behavior, and the leading value.

Write polynomials using conjugate roots and factorization, moving between linear factors, irreducible real factors, and standard form.

Use Descartes’ Rule of Signs and the Rational Root Theorem to predict and test roots efficiently, speeding up polynomial solving.

Discover how roots, factors, and end behavior shape the graph of a fifth-degree polynomial.

Explore polynomial graphs through continuity, smoothness, turning points, roots, and end behavior.

Use synthetic substitution to quickly evaluate polynomials at complex numbers and connect the process to the remainder theorem.

Teach students to use graphing calculators to model real problems and find quadratic maximums and minimums.

Learn how the sum and product of a quadratic’s roots connect quickly to its coefficients.

Help students understand when a quadratic is positive, negative, or zero using graphs, intervals, and inequalities.

Identify real or complex solutions by using the discriminant to predict the type of roots in any quadratic.

Learn to divide polynomials using long division and synthetic division for fast, reliable solutions.

Explore how vertex form controls parabola shifts, stretches, and reflections and connects to standard form.

Solve quadratics by completing the square and see how it leads to vertex form for graphing.

Solve quadratic equations using factoring and the quadratic formula, with clear steps for real and complex solutions.