Polynomials and the Factor Theorem | 30 Worked Examples | OCR B MEI A-Level Maths

30 fully worked questions on polynomials and the factor theorem for OCR B (MEI) A-Level Maths (H640), built for Year 12 students who want to expand, divide, factorise and sketch polynomials with confidence. The questions follow the style of the H640 papers, with command words such as Find, Show that, Determine and Hence, and seven questions carry the detailed reasoning instruction. The pack covers expanding and simplifying products of brackets, algebraic division by a linear factor such as (x - a) or (ax + b), using the factor theorem to show a linear expression is a factor, finding unknown coefficients from one or two given factors, fully factorising cubics and quartics, solving polynomial equations, showing that a cubic has exactly one real root, sketching cubics and quartics with repeated roots and negative leading coefficients, and finding where a line meets a cubic curve. Every solution is broken into single steps with a plain English reason, an arrow note on every line and OCR style M1, A1 and B1 marks placed exactly where a mark scheme rewards them, so students see how marks are earned and where they are lost. Several solutions include a clearly labelled sketch. The total is 168 marks. Ideal for homework, revision, tutoring or self study, and a complete answer for every question is included.

What’s inside:
Easy: 10 questions on expanding brackets, dividing by a linear factor, the factor theorem, factorising simple cubics and a first sketch
Medium: 13 questions on unknown coefficients, solving cubics and quartics, one real root, repeated roots, sketching and a line meeting a cubic
Hard: 7 questions on multi-part quartics, tangent lines, a cuboid volume, reading a cubic from its graph, surd answers and a family of cubics with a parameter