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Learn Factorisation method

Splitting and Solving Equations by Factorisation video thumbnail

Splitting and Solving Equations by Factorisation

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.

Factorisation Method: Splitting the Middle Term Equation: x² + 5x + 6 = 0 (a=1, b=5, c=6) Split: x² + 2x + 3x + 6 = 0 Group: x (x + 2) + 3 (x + 2) = 0 Factor: (x + 2) (x + 3) = 0 Roots: x = -2 , x = -3 The Logic: Splitting 5x Product (a × c) = 1 × 6 = 6 Sum (b) = 5 ∴ Chosen Factors: +2 and +3 Exam Tip! In board exams, clearly show the splitting step. Skipping directly to factors may lose you marks!

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!


Other Concepts in Quadratic Equations


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Splitting and Solving Equations by Factorisation video thumbnail

Splitting and Solving Equations by Factorisation

CBSE - Class 10>Mathematics>Quadratic Equations>Factorisation method


Splitting and Solving Equations by Factorisation video thumbnail

Splitting and Solving Equations by Factorisation

CBSE - Class 10>Mathematics>Quadratic Equations>Factorisation method

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Top Tutors who teach Factorisation method

Akshay Aggarwal Class 10 Tuition trainer in Delhi
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11 yrs of Exp 132 students
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Chaarvi Bansal

Akshay sir is a wonderful teacher, incredibly attentive towards the needs of students, he genuinely cares about them and makes efforts which most teachers would not do which motivates students to work harder. He has taught me science for two years and has changed the way I view the subject, as he encourages questions and interest for the topic outside of just the syllabus and is always willing to try and answer any questions I have!

Skills: Mathematics , Physics and more
Also teaches: Class 7 Tuition, Class 12 Tuition and more

(46)
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15 yrs of Exp 57 students
greenClock 3365 hrs of classes completed
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Maths and Science for 10th std. Score 💯
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With a decade of experience in teaching mathematics, physics, and chemistry for students from grades 8 through 12 across CBSE, IB, and ICSE boards, I offer a comprehensive educational approach that caters to a diverse range of curricula and learning needs. My academic background includes a BE and an MBA, equipping me with both technical and managerial skills that enhance my teaching methodology. Throughout my career, I have specialized in home tutoring, where I have developed a personalized approach to education that focuses on each student's unique needs and strengths. My sessions are designed to be interactive and engaging, fostering a learning environment where students feel supported and motivated. I conduct both online and offline classes, each lasting one hour, and utilize a variety of teaching tools to facilitate learning. I employ a whiteboard to visually explain concepts and provide question papers to help students practice and prepare for their exams. This hands-on approach ensures that students not only understand theoretical concepts but also develop problem-solving skills and confidence in their subjects. My commitment to delivering high-quality education and my extensive experience make me well-suited to guide students through their academic journey, helping them achieve their full potential in mathematics, physics, and chemistry.

Skills: Mathematics , Physics and more
Also teaches: BCom Tuition, Class 8 Tuition and more

Jayesh Chaudhari Class 10 Tuition trainer in Mumbai
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13 yrs of Exp 30 students
greenClock 1074 hrs of classes completed
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**Teaching Methodology:** My approach to teaching Mathematics and Science is personalized and interactive. I focus on understanding each student's unique learning style and adapt my methods accordingly. My goal is to make Maths and Science relatable and engaging, using real-life examples and practical applications to enhance understanding.I try to develop self thinking on problem and pushing them to solve by self **Key Skills:** - Strong grasp of Mathematics concepts across various levels - Ability to simplify complex topics for better understanding - Excellent communication and motivational skills - Patient and supportive, ensuring a comfortable learning environment - Regular progress assessments and constructive feedback **Services Offered:** - One-on-one personalized tutoring sessions - Homework and assignment assistance - Exam preparation and revision classes - Online and in-person tutoring options - Flexible scheduling to accommodate student needs **Achievements:** - Helped students improve their grades by an average of [25%] - Successfully prepared students for competitive exams with [JEE,NEET,IMO] - Received positive feedback and high ratings from students and parents Interested in improving your Maths AND Science skills? Contact me today to schedule a session and take the first step towards mastering Mathematics and Science!

Anagha Anil kadam

Excellent teaching method. Very focused and involved in kids / student. The teaching method which sir follow is extremely well and sensible.

Skills: Mathematics , Physics and more
Also teaches: Class 9 Tuition, Math Olympiad and more

Deepashree . Class 10 Tuition trainer in Bangalore
(220)
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12 yrs of Exp 11 students
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A professional trainer with 12 years of experience in STATE CBSE and ICESE board syllabus
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With over 15 years of dedicated teaching experience, I am an accomplished and qualified educator specializing in Spoken English, Math, Science, Social Science, and Kannada Language. My expertise extends across various educational boards, including CBSE, ICSE, and state boards. Passionate about unraveling the mysteries of mathematical problems and chemical equations. I have garnered recognition with the prestigious Best Teacher Award for orchestrating state-level Science exams. Having contributed my skills to the esteemed MaxMuller Public School in Bangalore, I am committed to fostering a nurturing and inspiring learning environment. Join me on this educational journey where knowledge meets enthusiasm!

Chiranjeevi

Enrolled my 10-year-old for math tutoring, and the improvement is remarkable. The tutor identifies weak spots quickly, like multiplication tables. Fun drills with timers make practice competitive and enjoyable. She explains errors without blame, turning mistakes into lessons. Custom worksheets align with his CBSE curriculum spot-on. Confidence boost evident; he volunteers answers in class now. Test scores rose steadily over two months. Responsive to parent queries, even on weekends. Affordable rates for such quality one-on-one attention. Planning long-term enrollment—excellent choice!

Skills: English , Mathematics and more
Also teaches: Yoga, Kannada Language and more

Sai V. Class 10 Tuition trainer in Madappanahalli
(138)
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locationImg Itagalpura Main Rd, Madappanahalli
17 yrs of Exp 131 students
greenClock 3515 hrs of classes completed
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MSc, BEd , (Phd), Member of Royal Society UK
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I gained extensive experience in delivering high-quality education following the CBSE/ICSE curriculum. My key responsibilities included: Classroom Teaching: Effectively taught Mathematics, Physics and Chemistry to students of classesX, ensuring alignment with the CBSE/ ICSE syllabus and fostering a deep understanding of key concepts. Curriculum Planning: Designed and implemented lesson plans that adhered to the CBSE guidelines, ensuring comprehensive coverage of topics while keeping in mind the varying learning needs of students. Student Assessment: Created and administered tests, quizzes, and assignments in accordance with the CBSE exam pattern. Monitored student performance and provided constructive feedback to facilitate continuous improvement. Interactive Learning: Encouraged an interactive classroom environment, integrating various teaching aids such as multimedia presentations, hands-on activities, and group discussions to enhance student engagement and understanding. Preparation for Board Exams: Provided focused support for students appearing for their CBSE/ICSE board exams by conducting regular revision sessions, mock tests, and personalized guidance to help them excel. Parental Communication: Maintained regular communication with parents regarding student progress, attendance, and overall development. Organized parent-teacher meetings to ensure a collaborative approach to student growth. Co-curricular Involvement: Actively participated in school events, projects, and extracurricular activities, fostering holistic development among students. Professional Development: Engaged in continuous professional development through workshops and CBSE training programs to stay updated with the latest educational practices and policies.

Skills: Mathematics , Physics and more
Also teaches: Class 12 Tuition, Class 11 Tuition and more

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FAQ

What is the meaning of Factorisation method?

It refers to a specific mathematical method or property in Quadratic Equations used to solve problems involving Factorisation method.

Why is Factorisation method important for CBSE - Class 10 exams?

This concept is crucial for the exams as questions related to Quadratic Equations and specifically Factorisation method are very common. It helps secure marks in the section effectively.

Is Factorisation method part of the latest NCERT syllabus?

Yes, Factorisation method is an integral part of the CBSE - Class 10 NCERT Mathematics syllabus. It is a key topic covered in the Quadratic Equations chapter.

What are common mistakes students make with Factorisation method?

Students often miss the minute details or fundamental definitions of Factorisation method. Regular revision and practice are needed to master the nuances.

How should I approach learning Factorisation method?

Start by understanding the formulas and logic, then practice applying them to simple problems. Solve the examples given in the NCERT textbook before moving to exercise problems.

How can UrbanPro help me understand Factorisation method better?

UrbanPro connects you with experienced Mathematics tutors who can explain Factorisation method with simple examples. You also get access to doubt-clearing sessions and mock tests for better preparation.

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