How can I double check my math answers?

Resolve equations using alternative methods (e.g., check quadratic roots by plugging them back into ax² + bx + c), verify decimals using scientific solvers, and review step-by-step worked calculations.

Where are these syllabus concepts applied in real life?

Trigonometry is used in architecture, mechanics and navigation. Quadratic equations model rocket trajectories and profit boundaries. Basic arithmetic and fractions are applied in accounting, budgeting and lab chemistry.

Back to Class VIII Mathematics

Class VIII Mathematics

Chapter 12: Factorisation

Standard NCERT & CBSE aligned study curriculum. Master concepts, track accuracy, revise weak areas, and challenge yourself with 9 customized practice modes.

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Syllabus Sections

Chapter Overview

Welcome to Class VIII Mathematics: Factorisation. This chapter forms a core structural component of the math syllabus, designed to build analytical rigor and key formula models.

Use the detailed subtopic guide below to review standard definitions, key mathematical rules, and study guidelines.

Prerequisite Concepts

Algebraic Expressions and IdentitiesAlgebraic Expressions

Detailed Subtopics Study Guide

Review detailed conceptual explanations, mathematical equations, and guidelines for each subtopic in this chapter:

1Factors of algebraic expressions

Concept Explanation

Finding the product components that make up an algebraic expression, written in factored form.

Mathematical Representation

ax + bx = x(a+b)

Study Guideline: Examine the terms to find common numeric or variable factors.

2Common factors regrouping

Concept Explanation

Factorizing by grouping terms in sets of two that share common binomial factors.

Mathematical Representation

ab + a + bc + c = a(b+1) + c(b+1) = (a+c)(b+1)

Study Guideline: Rearrange terms if a common binomial does not immediately appear after grouping.

3Factorisation using identities

Concept Explanation

Using standard algebraic identities to write quadratic trinomials in factored form.

Mathematical Representation

a^2 - b^2 = (a-b)(a+b), \quad a^2 \pm 2ab + b^2 = (a \pm b)^2

Study Guideline: Identify if terms match a difference of two squares or a perfect square trinomial.

4Split middle term factorisation

Concept Explanation

Factorizing quadratic trinomials of the form x² + px + q by finding two numbers that add to p and multiply to q.

Mathematical Representation

x^2 + (a+b)x + ab = (x+a)(x+b)

Study Guideline: To factor x² + 5x + 6, find two numbers that multiply to 6 and add to 5 (which are 2 and 3).

5Division of algebraic expressions (monomial/polynomial)

Concept Explanation

Dividing algebraic expressions by factoring terms completely and cancelling out common factors.

Mathematical Representation

\frac{A(x)}{B(x)} = Q(x)

Study Guideline: Factor the numerator and denominator fully before cancelling out common brackets.