IB Maths AHL 2.12 - Polynomial Functions and Equations

This IB Maths AA AHL Topic 2.12 – Polynomial Functions and Equations resource introduces students to polynomial functions and develops confidence in connecting their algebraic and graphical features. It begins by defining polynomial functions and showing how degree and leading coefficient affect end behaviour, before guiding students through the relationship between zeros, roots, factors, and x-intercepts. Students are also introduced to multiplicity, including how repeated roots can cause a graph to touch rather than cross the x-axis.

The lesson then develops key AHL skills through the factor theorem, remainder theorem, polynomial factorisation, and Vieta-style relationships between coefficients and roots. Students practise identifying roots graphically and algebraically, testing whether a linear expression is a factor, finding remainders, solving for unknown coefficients, and using the sum and product of roots without fully solving the polynomial. With clear explanations, worked examples, graph interpretation, structured practice questions, exam tips, and fully worked solutions, this resource helps AHL students build a strong understanding of polynomial functions, graphs, and equations in line with IB Mathematics AA expectations.