Gujarat Board Class 10 Mathematics — Flashcards for Quick Revision

A: Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur. For example: 12 = 2² × 3 (this is

A: It means that for any composite number, there is one and only one way to write it as a product of primes (ignoring the order). For example, 30 can only be written as 2 × 3 × 5, regardless of the order

A: 32760 = 2³ × 3² × 5 × 7 × 13. This is found by factorising: 32760 = 2 × 2 × 2 × 3 × 3 × 5 × 7 × 13 = 2³ × 3² × 5¹ × 7¹ × 13¹

A: A polynomial is an algebraic expression consisting of variables and coefficients, combined using only addition, subtraction, multiplication, and non-negative integer exponents. Example: 2x³ - 5x² + 3x

A: The degree of a polynomial is the highest power of the variable in the polynomial. For 5x³ - 4x² + x - √2, the highest power of x is 3, so the degree is 3.

A: A linear polynomial is a polynomial of degree 1. Examples: (1) 2x - 3, (2) √3x + 5, (3) y + √2. General form: ax + b where a ≠ 0.

A: A linear equation in two variables is an equation that can be written in the form ax + by + c = 0, where a, b, and c are real numbers and a and b are not both zero. Examples: 2x + 3y - 5 = 0, x - 4y +

A: A pair of linear equations in two variables consists of two linear equations with the same two variables. For example: a₁x + b₁y + c₁ = 0 a₂x + b₂y + c₂ = 0 Where x and y are the same variables in bot

A: A pair of linear equations in two variables that has at least one solution is called a consistent pair of linear equations. This means the equations can be satisfied by some values of x and y.