Polynomials Notes: Class 9 Maths Chapter 2
Class 9 Maths Chapter 2 Polynomials covers polynomials in one variable, zeroes of a polynomial, the Remainder Theorem, the Factor Theorem, and algebraic identities used for factorisation.
Overview of Topics & Subtopics (Click to Jump)
1. Polynomials in One Variable
Short Note:
• A polynomial in one variable x is an expression of the form anxn + ... + a1x + a0, where a0, a1, ... are real numbers and the exponents are non-negative integers.
• Degree: the highest power of the variable in a polynomial.
• Based on degree: Linear (degree 1), Quadratic (degree 2), Cubic (degree 3) polynomials.
• Based on number of terms: Monomial (1 term), Binomial (2 terms), Trinomial (3 terms).
2. Zeroes of a Polynomial
Short Note:
• A real number k is a zero of polynomial p(x) if p(k) = 0.
• A linear polynomial has exactly one zero, a quadratic polynomial has at most two zeroes, and in general a polynomial of degree n has at most n zeroes.
3. Remainder Theorem & Factor Theorem
Short Note:
• Remainder Theorem: If p(x) is divided by (x − a), the remainder is p(a).
• Factor Theorem: (x − a) is a factor of p(x) if and only if p(a) = 0.
4. Algebraic Identities
Short Note:
• (x + y)² = x² + 2xy + y²
• (x − y)² = x² − 2xy + y²
• x² − y² = (x + y)(x − y)
• (x + y)³ = x³ + y³ + 3xy(x + y)
• (x − y)³ = x³ − y³ − 3xy(x − y)
• x³ + y³ + z³ − 3xyz = (x + y + z)(x² + y² + z² − xy − yz − zx)
NCERT Textbook Exercise Questions
(ii) y + 2/y is not a polynomial because it contains y−1, a negative exponent.