This IB Maths AA HL Topic AHL 2.12 – Polynomial Functions and Equations resource develops students’ understanding of polynomial equations and the relationships between their roots, zeros, factors, and graphical representations. It begins by reviewing the general form of a polynomial and how its degree and leading coefficient influence its end behaviour. Students then learn how roots correspond to x-intercepts and linear factors, including how repeated roots and multiplicity affect whether a graph crosses or touches the x-axis.

The lesson also develops confidence in using the Factor Theorem and Remainder Theorem to test factors, calculate remainders, determine unknown coefficients, and fully factorise polynomial expressions. Students explore Vieta-style relationships between the coefficients of a polynomial and the sum and product of its roots, before applying these ideas to construct polynomial equations from given roots and points. With clear explanations, worked examples, graphical and algebraic practice, exam tips, and fully worked solutions, this resource helps HL students build strong polynomial reasoning in line with IB Mathematics AA expectations.