Polynomials and Factorisation — Chapter Summary
Telangana Board · Class 9 · Mathematics
Summary of Polynomials and Factorisation for Telangana Board Class 9 Mathematics. Part of the Telangana Board Class 9 Mathematics syllabus.
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Overview
Polynomials are fundamental algebraic expressions that form the backbone of advanced mathematics. This chapter introduces you to polynomial expressions, their classification, properties, and factorisation techniques. You'll learn to work with algebraic expressions systematically, understand the rela
Key Concepts
A polynomial is an algebraic expression
A polynomial is an algebraic expression where variables have only non-negative integer powers. Examples: 3x² + 2x - 1 (polynomial), x^(-1) + 2 (not po
By degree
By degree: Linear (degree 1): ax + b; Quadratic (degree 2): ax² + bx + c; Cubic (degree 3): ax³ + bx² + cx + d. By terms: Monomial (1 term): 5x²; Bino
A zero of polynomial p(x)
A zero of polynomial p(x) is a value 'a' where p(a) = 0. Step-by-step process: 1) Set polynomial equal to zero, 2) Solve for variable, 3) Verify by su
When polynomial p(x) is divided by
When polynomial p(x) is divided by (x - a), remainder = p(a). Step-by-step application: 1) Identify the divisor (x - a), 2) Find 'a' by setting x - a
(x
(x - a) is a factor of p(x) if and only if p(a) = 0. Two-way relationship: If p(a) = 0, then (x - a) is a factor; If (x - a) is a factor, then p(a) =
Learning Objectives
- Understand what polynomials are and identify them from general algebraic expressions
- Classify polynomials based on degree (linear, quadratic, cubic) and number of terms (monomial, binomial, trinomial)
- Find the degree and coefficients of polynomials accurately
- Calculate the value of polynomials for given variable values
- Find zeros (roots) of polynomials and understand their significance
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Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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