Remainder and Factor Theorems — Class 10 ICSE Mathematics revision notes
A 3-page visual revision sheet for Remainder and Factor Theorems, written for Class 10 ICSE Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
What this Remainder and Factor Theorems sheet covers
- Division of a polynomial
- Remainder Theorem
- p(x) divided by x - a
- divided by x + a
- divided by ax - b
- divided by ax + b
- why: put x = a in the division
- Factor Theorem
- if p(a) = 0
- and conversely, if (x - a) is a factor
- (ax - b) is a factor exactly when
- (x + a) is a factor exactly when
- Shortcuts that come from the theorems
- Finding remainders
- Finding k from a factor, then factorising
- Two unknowns from two conditions
- Factorising Cubic Polynomials
- Factorising a cubic
- A cubic with leading coefficient 1
- Synthetic division of 2x³ + x² - 13x + 6 by x - 2
- A cubic with leading coefficient 2
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Remainder and Factor Theorems the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.