Schooling · Class 9 · Mathematics · Introduction to Linear Polynomials · Chapter on a page
CBSE Class 9 · Mathematics · NCERT Ganita Manjari
Introduction to Linear Polynomials: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- A polynomial in one variable x is an…
- The degree of a polynomial is the…
- A linear polynomial has degree 1 and…
- Polynomials are named by the number…
- The value of a polynomial p(x) at x…
- A zero of a polynomial p(x) is a…
- Expressions like 1/x, √x, or x^(−2)…
- Formulas and facts
- Formula or fact
- Zero of ax + b is x = −b/a
- Degree of zero polynomial: not defined
- p(k) means substitute x = k in p(x)
- Watch out for
- Thinking x⁻¹ or 1/x is a polynomial
- Confusing degree with number of terms
- Writing the zero of ax + b as b/a…
- Believing every algebraic expression…
- Forgetting that a non-zero constant…
What this chapter is about
This chapter introduces you to polynomials, which are algebraic expressions built from variables and constants using addition, subtraction and multiplication. You will learn to identify different types of polynomials based on the number of terms they have and the highest power of the variable they contain. The focus is on linear polynomials, where the highest power of the variable is one.
Key ideas
- A polynomial in one variable x is an expression of the form a₀ + a₁x + a₂x² + ... + aₙxⁿ, where a₀, a₁, a₂, ... are constants (called coefficients) and n is a whole number.
- The degree of a polynomial is the highest power of the variable with a non-zero coefficient. For example, 5x³ + 2x − 7 has degree 3.
- A linear polynomial has degree 1 and takes the general form ax + b, where a ≠ 0. Examples: 3x + 4, −2x + 1, x − 5.
- Polynomials are named by the number of terms: a monomial has one term, a binomial has two terms, and a trinomial has three terms.
- The value of a polynomial p(x) at x = k is found by substituting k for x. This value is written as p(k).
- A zero of a polynomial p(x) is a number k such that p(k) = 0. For a linear polynomial ax + b, the zero is x = −b/a.
- Expressions like 1/x, √x, or x^(−2) are not polynomials because they involve negative or fractional powers of the variable.
Formulas and facts to remember
- Formula or fact: General form of linear polynomial: ax + b, where a ≠ 0 · Meaning: A polynomial with degree exactly 1
- Formula or fact: Zero of ax + b is x = −b/a · Meaning: The value of x that makes the polynomial equal to zero
- Formula or fact: Degree of a constant polynomial (non-zero): 0 · Meaning: A number like 7 or −3 is a polynomial of degree zero
- Formula or fact: Degree of zero polynomial: not defined · Meaning: The polynomial 0 has no defined degree
- Formula or fact: p(k) means substitute x = k in p(x) · Meaning: How to evaluate a polynomial at a specific point
Common mistakes
- Thinking x⁻¹ or 1/x is a polynomial → it is not, because the power of x must be a non-negative whole number.
- Confusing degree with number of terms → degree is about the highest power, not how many terms exist.
- Writing the zero of ax + b as b/a instead of −b/a → always take the negative of b divided by a.
- Believing every algebraic expression is a polynomial → expressions with √x or x in the denominator are not polynomials.
- Forgetting that a non-zero constant like 7 is also a polynomial (of degree 0) → constants are polynomials with no variable term.
Quick revision
- A polynomial has only whole-number powers of the variable.
- Degree = highest power of x with a non-zero coefficient.
- Linear polynomial: ax + b (a ≠ 0), degree 1.
- Zero of ax + b is found by solving ax + b = 0, giving x = −b/a.
- To find p(k), substitute k wherever x appears and simplify.