Knowledge organisers

Introduction to Polynomials: CBSE Class 9 Maths knowledge organiser

Everything to know about introduction to polynomials on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Polynomial: An expression of terms axⁿ where every power n is a whole number.
Degree: The highest power of the variable with a non-zero coefficient.
Zero of a polynomial: A value of x that makes p(x) = 0.

Key formulas

Polynomial: degree = highest power; linear polynomial and its zero	\(p(x)=ax+b\ (a\ne0);\) \(x=-\frac ba\)
Line \(y=ax+b\): slope \(a\), \(y\)-intercept \(b\)	\(a=\frac{y_2-y_1}{x_2-x_1}\)
Linear growth (\(a>0\)) / decay (\(a<0\)): equal change per equal step

Worked example

Find the linear polynomial \(p(x)\) with \(p(0) = 4\) and \(p(3) = 13\).

\(b = 4\) and \(3a + 4 = 13 \Rightarrow a = 3\), so \(p(x) = 3x + 4\).

Common mistakes

Calling \(x + \dfrac1x\) or \(\sqrt x\) a polynomial: the powers must be whole numbers.
Reading the slope of \(y = 5 - 3x\) as \(5\): the slope is the coefficient of \(x\), here \(-3\).
Slope as \(\dfrac{x_2 - x_1}{y_2 - y_1}\) (upside down), or mixing the order of the points in numerator and denominator.
In word problems, using the value after one step as the starting value \(b\).

You should be able to…

Recognise polynomials and their degree, evaluate p(c) and read slope and intercept from y = ax + b.
Build a linear model from a table or a story and find a zero, a slope or an unknown coefficient.
Compare two linear models and answer every part of a growth or decay case study.
Find a line from two conditions, its intercepts and the area it cuts off, and reason about degree.

The printable sheet

Introduction to Polynomials knowledge organiser for CBSE Class 9 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Introduction to Polynomials knowledge organiser (CBSE Class 9 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 9 Maths topics: Number System · Sequences and Progressions · Exploring Algebraic Identities · Linear Equations in Two Variables · Coordinate Geometry · Introduction to Euclid's Geometry: Axioms and Postulates · Lines and Angles · Triangles – Congruence Theorems · 4-gons (Quadrilaterals) · Circles · Area and Perimeter · Surface Area and Volume · Statistics · Introduction to Probability · All CBSE Class 9 Maths organisers