Algebra

Polynomials, Equations, Exponents and Algebraic Identities

---

Overview

Algebra forms the backbone of mathematics at the upper primary level (Classes 6–8) and is a high-scoring area in TN TET Paper II. This topic tests your ability to manipulate symbols, simplify expressions, solve equations and apply standard identities—skills every mathematics teacher must demonstrate confidently.

For TN TET, expect questions on identifying polynomial types, finding values of expressions using identities, solving linear equations and simplifying exponential expressions. The pedagogy section may also ask how to introduce algebraic concepts to young learners. Mastery here requires fluency with rules and the ability to spot shortcuts using identities.

The scope covers four interconnected areas: polynomials (classification and operations), equations (linear equations in one and two variables), exponents (laws of indices) and algebraic identities (standard expansions and factorisations). A strong grip on these fundamentals makes higher mathematics accessible to students.

---

Key Concepts

• **Variable and Constant**: A variable (x, y) can take different values; a constant (3, –7) has a fixed value. Algebraic expressions combine both using operations.

• **Polynomial**: An expression with one or more terms where variables have whole-number exponents. Example: 3x² + 5x – 2. Polynomials are classified by degree (highest power) and number of terms.

• **Degree of a Polynomial**: The highest exponent of the variable. For 4x³ – x + 7, degree = 3. A constant non-zero polynomial has degree 0; zero polynomial has no defined degree.

• **Types by Terms**: Monomial (1 term), Binomial (2 terms), Trinomial (3 terms). Example: 5x is monomial; x + 1 is binomial; x² + x + 1 is trinomial.

• **Linear Equation**: Equation of degree 1. Standard form: ax + b = 0 (one variable) or ax + by + c = 0 (two variables). Solution is the value making LHS = RHS.

• **Exponent (Index/Power)**: In aⁿ, 'a' is base and 'n' is exponent. Exponents indicate repeated multiplication: 2⁴ = 2 × 2 × 2 × 2 = 16.

• **Algebraic Identity**: An equation true for all values of the variables. Unlike an equation (true for specific values), identities are universally valid and used for quick expansion/factorisation.

• **Zero of a Polynomial**: Value of variable that makes polynomial equal to zero. For p(x) = x – 3, zero is x = 3 because p(3) = 0.

---

Formulas / Key Facts

### Laws of Exponents (a, b ≠ 0; m, n are integers)