Mathematics · Class 9
Polynomials
Polynomial degrees, zeroes, remainder theorem, and factorisation.
4 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Polynomials are expressions built from variables and coefficients using addition, subtraction, and non-negative integer powers. Class 9 covers types of polynomials, zeroes, factorisation, and algebraic identities.
Types and Degree
- Linear (degree 1): ax + b
- Quadratic (degree 2): ax² + bx + c
- Cubic (degree 3): ax³ + bx² + cx + d
- Zero polynomial has degree not defined
Zeroes and Factorisation
- Zero of p(x) is a where p(a) = 0
- Factor theorem: (x − a) is factor iff p(a) = 0
- Split middle term or use identities to factorise
Key Identities
(x + y)²
x² + 2xy + y²
(x − y)²
x² − 2xy + y²
x² − y²
(x + y)(x − y)
(x + a)(x + b)
x² + (a + b)x + ab
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Find zeroes
Find zeroes of p(x) = x² − 5x + 6.
- 1Factorise: (x − 2)(x − 3)
- 2Set each factor to zero
- 3x = 2 or x = 3
Answer
Zeroes: 2 and 3
Example 2: Expand
Expand (2x − 3)².
- 1Use (a − b)² = a² − 2ab + b²
- 2(2x)² − 2(2x)(3) + 3²
- 3= 4x² − 12x + 9
Answer
4x² − 12x + 9
Key Points to Remember
- ✓ Degree is highest power of variable
- ✓ A polynomial of degree n has at most n zeroes
- ✓ Remainder theorem: p(x) ÷ (x − a) gives remainder p(a)
Exam Tips
- • Verify factorisation by expanding back
- • Use identities before long multiplication
- • State degree when classifying polynomials
Practice MCQs — Polynomials
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
Degree of 5x³ − 2x + 7 is: