What is it
Polynomials at A-Level covers dividing polynomials, using the factor theorem to find roots, and sketching polynomial graphs based on their roots and behaviour at extreme values of x.
Why it matters
Polynomial division and the factor theorem are the algebraic tools used to solve cubic and higher-degree equations — problems that can't be factorised by inspection the way GCSE quadratics can.
Exam tip
Always test small integer values (±1, ±2, ±3) first when using the factor theorem to find a root — most exam-set polynomials are deliberately designed to have a small, easy-to-find first root.
Related topics
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