Polynomials — Class 9 Maharashtra SSC Mathematics revision notes
A 4-page visual revision sheet for Polynomials, written for Class 9 Maharashtra SSC 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.
Page 1 as PDF
Polynomials in one look
expressions built from whole number powers, how they divide, and the theorems that save the division
What counts as a polynomial
- a polynomial in x is a sum of terms of the form ax^n where every n is a whole number and a is a real coefficient
- so 3x^2 - 5x + 2 is a polynomial, but x^-1 and √x are not, because their powers are not whole numbers
- a variable in a denominator disqualifies the expression too, since that is a negative power in disguise
- the degree is the highest power of the variable appearing with a non zero coefficient
- the leading coefficient is the number multiplying that highest power, and the constant term is the one with no variable
- a zero polynomial is just 0, and its degree is not defined
Naming a polynomial two ways
| Degree | Called | Example |
|---|---|---|
| 0 | constant | 7 |
| 1 | linear | 2x + 3 |
| 2 | quadratic | x² - 5x + 6 |
| 3 | cubic | x³ + 2x - 1 |
| 4 | biquadratic | x⁴ - 16 |
The identities that do most of the work
- square of a sum
(a+b)^2 = a^2 + 2ab + b^2 - square of a difference
(a-b)^2 = a^2 - 2ab + b^2 - difference of two squares
a^2 - b^2 = (a+b)(a-b) - cube of a sum
(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 - sum of two cubes
a^3 + b^3 = (a+b)(a^2 - ab + b^2) - difference of two cubes
a^3 - b^3 = (a-b)(a^2 + ab + b^2)
Page 1 of 4. The full sheet, all 4 pages, opens free in the app.
What this Polynomials sheet covers
- Polynomial
- Degree
- Coefficient
- What counts as a polynomial
- Naming a polynomial two ways
- The identities that do most of the work
- square of a sum
- square of a difference
- difference of two squares
- cube of a sum
- sum of two cubes
- difference of two cubes
- Value of a polynomial
- Zero of a polynomial
- The value of a polynomial, and its zeroes
- Remainder theorem
- Factor theorem
- The remainder and factor theorems
- Using the remainder theorem
- Factorising a cubic completely
- Division of polynomials
- Synthetic division
- Dividing one polynomial by another
- Terms in this chapter
- 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 Polynomials 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.