Learn Factorisation method

In the CBSE Class 10 Mathematics curriculum, mastering Quadratic Equations is a critical milestone, and the Factorisation Method is often the first and most fundamental technique taught to solve them. A quadratic equation is a polynomial equation of degree 2, typically written in the standard form ax² + bx + c = 0. The factorisation method, commonly known as "splitting the middle term," involves breaking down this complex equation into a product of two simpler linear binomials. By simplifying the expression in this way, you can easily find the roots (or solutions) of the equation, which graphically represent the exact points where the quadratic curve intersects the x-axis.

The core logic of the factorisation method relies on strategically manipulating the middle term, bx. To successfully factorise ax² + bx + c = 0, you must find two distinct numbers—let's call them p and q. These two numbers must satisfy two strict mathematical conditions: their sum must exactly equal the middle coefficient (p + q = b), and their product must equal the product of the first and last coefficients (p × q = a × c). Once you successfully identify these numbers, you split the bx term into px + qx. From there, you group the terms in pairs and factor out the greatest common elements, transforming the equation into the form (x - r₁)(x - r₂) = 0. Finally, by applying the zero-product property, you set each factor to zero to find your final roots.

The diagram above visually breaks down the entire factorisation workflow using the example equation x² + 5x + 6 = 0. On the right side, the logic box demonstrates how we apply the sum and product rules: we need two numbers that multiply to 6 (the product of a and c) and add up to 5 (the middle term b). The numbers 2 and 3 perfectly fit this criteria. Following the sequence on the left, you can see how the original 5x is logically split into 2x + 3x. The most critical step occurs during "Grouping," where the common binomial expression (x + 2)—highlighted in red—is successfully factored out. In CBSE Class 10 board exams, questions utilizing this specific method are highly prevalent in 2-mark and 3-mark sections. Examiners specifically look for the explicit middle-term splitting step; skipping directly to the final roots can result in a deduction of marks. This method is also a highly essential building block for solving more complex word problems related to age, distance, and geometry.

Mastering the factorisation method takes dedicated practice, and sometimes, a little expert guidance can make all the difference in understanding the core logic. If you find yourself struggling with quadratic equations, polynomials, or simply want to secure top marks in your upcoming board exams, consider connecting with experienced, verified CBSE Class 10 Mathematics tutors on UrbanPro. Whether you prefer personalized one-on-one online tuition or interactive local offline classes, the UrbanPro platform helps you effortlessly find top-rated educators tailored to your learning style. An expert tutor can help simplify complex math concepts, provide structured practice sheets, and drastically build your problem-solving confidence. Explore highly qualified tutors on UrbanPro today and take total control of your academic success!