RS Aggarwal Solutions Class 8 Chapter-7 Factorisation (Ex 7C) Exercise 7.3 - Free PDF
FAQs on RS Aggarwal Solutions Class 8 Chapter-7 Factorisation (Ex 7C) Exercise 7.3
1. What is the main technique used to solve problems in RS Aggarwal Class 8 Maths Chapter 7, Exercise 7C?
The primary technique for Exercise 7C is the factorisation of quadratic trinomials of the form x² + px + q. This method is commonly known as 'splitting the middle term'. It involves finding two numbers whose product equals the constant term 'q' and whose sum equals the coefficient of the middle term 'p'. Mastering this single method is key to solving all the questions in this specific exercise.
2. How do you correctly choose the two numbers when splitting the middle term in a trinomial from Ex 7C?
To correctly choose the two numbers for a trinomial like x² + px + q, follow these steps as per the CBSE 2025-26 curriculum guidelines:
- First, find all the factor pairs of the constant term 'q'.
- Next, from these pairs, identify the one pair that adds up to the middle term's coefficient, 'p'.
- Pay close attention to the signs. If 'q' is positive, both numbers have the same sign as 'p'. If 'q' is negative, the numbers have opposite signs, with the larger number taking the sign of 'p'.
For example, in x² + 5x + 6, the factors of 6 are (1,6) and (2,3). The pair (2,3) sums to 5, so these are the correct numbers to use.
3. What types of questions can I expect in RS Aggarwal Class 8 Chapter 7, Exercise 7.3 (7C)?
Exercise 7.3 (7C) exclusively contains questions on factorising quadratic trinomials where the coefficient of the squared term is 1. The problems will vary in terms of the signs of the middle term and the constant term, testing your ability to correctly apply the 'splitting the middle term' method in different scenarios involving positive and negative integers.
4. What is a common mistake students make when factorising trinomials with negative terms in Ex 7C?
A very common mistake is mishandling the signs when choosing the factor pairs. For an expression like x² - 2x - 15, students might correctly find the factors of -15 (e.g., 5 and -3, or -5 and 3) but choose the wrong pair. The correct pair must sum to the middle coefficient, which is -2. Here, -5 + 3 = -2, making (-5, 3) the correct choice. Students often incorrectly choose (5, -3) which sums to +2, leading to an incorrect final answer.
5. How does solving RS Aggarwal Ex 7C help in building a strong foundation in algebra?
Mastering the solutions for Exercise 7C is crucial because it builds the foundational skill of factorising trinomials. This is not just a Class 8 topic; it is a fundamental prerequisite for more advanced topics in Class 9 and 10, including solving quadratic equations, simplifying rational expressions, and understanding polynomial functions. Getting this method right ensures you can handle more complex algebraic manipulations later.
6. Why is the 'splitting the middle term' method so important for the factorisation chapter?
The 'splitting the middle term' method is important because it is a versatile technique that works for trinomials that cannot be factorised using standard identities like (a+b)² or (a-b)². It essentially reverses the FOIL (First, Outer, Inner, Last) multiplication process. Understanding this method provides a systematic approach to break down complex expressions into simpler, irreducible factors, which is the core goal of factorisation.
7. Can all trinomials in Chapter 7 be factorised using the methods from Ex 7C?
No, not all trinomials can be factorised into integers. An expression is considered 'prime' if it cannot be broken down further into factors with integer coefficients. For a trinomial like x² + px + q, if you cannot find any pair of integer factors of 'q' that also sum up to 'p', the expression cannot be factorised using this method and is likely prime over the integers. All problems in RS Aggarwal Ex 7C are designed to be factorisable.
