Playbook
Polynomials
79 q · 19% HARD · about 3.8 a paper. The factor theorem has never set a HARD question; HCF and LCM of polynomials is the largest page and holds the most HARD.
- Questions in the bank
- 79
- q/paper (21 papers)
- 3.76
- Tagged HARD
- 19%
- Subtopics
- 5
Strand: Selective
When you’ll see it
A polynomial divided by (x − a), a factor to test, or the HCF and LCM of two expressions.
How this chapter is tested
79 questions, about 3.8 a paper, at 19% HARD. The factor theorem has never set a HARD question; HCF and LCM of polynomials is the largest page (25 questions) and holds 6 of the 15 HARD.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
Remainder theorem
The remainder on division by (x − a) is p(a).
Factor theorem
(x − a) is a factor exactly when p(a) = 0.
Factorisation
Splitting the middle term, and a³ ± b³.
HCF and LCM
Factorise both fully; HCF takes the common factors, LCM all of them.
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.
Dividing by (x + a)
Put x = −a, not +a.
HCF × LCM
For two polynomials it equals their product only up to a constant factor.
Learn it before you drill it
This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each subtopic. Read the notes once, then drill subtopic by subtopic below.
Polynomials notesDrill every Polynomials question
79 questions from the bank, across 5 subtopics.
Drill one subtopic at a time
The 5 subtopics, in teaching order.
- Degree, Zeros and CoefficientsDrill Degree, Zeros and Coefficients
- The Remainder TheoremDrill The Remainder Theorem
- The Factor TheoremDrill The Factor Theorem
- Factorisation of PolynomialsDrill Factorisation of Polynomials
- HCF and LCM of PolynomialsDrill HCF and LCM of Polynomials
Related playbooks
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