Chapter 2 — Introduction to Linear Polynomials

Chapter 2 of the Class 9 Maths NCERT textbook, "Introduction to Linear Polynomials", introduces univariate polynomials and their degree, then focuses on linear polynomials (degree 1) — linear patterns, growth and decay, relationships of the form y = ax + b, and plotting them as straight lines.

• Polynomials and Degree — Polynomials are algebraic expressions classified by the highest power of their variable. Degree sorts them into constant (0), linear (1), quadratic (2), and cubic (3), giving a framework for the whole chapter.
• Linear Polynomials in Depth — A degree-1 polynomial like 3z + 7 is the chapter's focus. Substituting a value evaluates it through an input-output process, turning the abstract expression into concrete numbers.
• Linear Patterns, Growth and Decay — Sequences where consecutive terms differ by a constant reveal linear behaviour. When the amount rises by a fixed step it is linear growth; when it falls by a fixed step it is linear decay.
• Straight-Line Relationships — A linear relationship is written y = ax + b and drawn as a straight line. The slope a controls its steepness and the y-intercept b fixes where it crosses the vertical axis.

1. 01The degree of a polynomial is the highest power of its variable
2. 02Polynomials by degree: constant 0, linear 1, quadratic 2, cubic 3
3. 03A linear polynomial has degree 1, such as 3z + 7 or 2x + 3
4. 04Evaluate a polynomial by substituting a value of the variable
5. 05A linear pattern has a constant difference between consecutive terms
6. 06Linear growth increases and linear decay decreases by a fixed amount
7. 07A linear relationship is y = ax + b, where a is slope and b the y-intercept