← GSEB Class 9
Polynomials
Chapter Overview
A polynomial p(x) in one variable x is an expression of the form a_n xn + a_(n-1) xn-1 + ... + a_1 x + a_0. The degree is the highest power of x. Constant, linear, quadratic, and cubic polynomials are classified by degree. The zero of a polynomial p(x) is a value k such that p(k) = 0. Remainder theorem: when p(x) is divided by (x - a), the remainder is p(a). Factor theorem: if p(a) = 0, then (x - a) is a factor. Factorization methods include common factors, regrouping, and algebraic identities.
Topics Covered
- Polynomial Definition
- Degree and Types
- Zeros of Polynomial
- Remainder Theorem
- Factor Theorem
- Factorization Methods
- Algebraic Identities
Key Formulas
(x + a)(x + b) = x2 + (a+b)x + ab
(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 - 2ab + b2
(a + b)(a - b) = a2 - b2
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
(a + b)3 = a3 + 3a2b + 3ab2 + b3
Real-World Applications
Applications: Curve fitting, computer graphics, physics formulas, engineering calculations.
Study Tips
Tip: Master the remainder and factor theorems
Tip: Practice algebraic identities thoroughly
Tip: Learn different factorization techniques