Last Updated on October 17, 2024 by XAM CONTENT
Hello students, we are providing case study questions for class 8 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 8 maths. In this article, you will find case study questions for CBSE Class 8 Maths Chapter 12 Factorisation . It is a part of Case Study Questions for CBSE Class 8 Maths Series.
| Chapter | Factorisation |
| Type of Questions | Case Study Questions |
| Nature of Questions | Competency Based Questions |
| Board | CBSE |
| Class | 8 |
| Subject | Maths |
| Useful for | Class 8 Studying Students |
| Answers provided | Yes |
| Difficulty level | Mentioned |
| Important Link | Class 8 Maths Chapterwise Case Study |
Case Study Questions on Factorisation
Questions
Passage 1:
Passage 1: Two brothers Anuj and Aman started a business together. They decided to share the capitals depending upon the variable expenditure. The capital of two brothers together is given by the polynomial p2 + 10p + 21, which is the product of their individual share factors.
Q. 1. The capital of the two partners when $p=8$ ?
(a) ₹872
(b) ₹1072
(c) ₹972
(d) ₹672
Ans. Option (b) is correct.
Explanation: 16 × 8 × 8 + 9 × 8 – 24
= 1024 + 72 – 24 = ₹ 1072
Q. 2. What is the individual share of both brothers?
(a) $(p+3)(p+7)$
(b) $(p-3)(p+7)$
(c) $(p+3)(p-7)$
(d) $(p-3)(p-7)$
Ans. Option (a) is correct.
Explanation: $p^2+10 p+21$
$$
=p^2+7 p+3 p+21
$$
$$
\begin{aligned}
& =p(p+7)+3(p+7) \\
& =(p+3)(p+7)
\end{aligned}
$$
Q. 3. What is the sum of their capitals?
(a) $2 p+5$
(b) $2 p+10$
(c) $2 p-5$
(d) $2 p-10$
Ans. Option (b) is correct.
$$
\begin{aligned}
& \text { Explanation: }(p+3)+(p+7) \\
& =p+3+p+7=2 p+10=2 p+10
\end{aligned}
$$
Q.4. If they changed the capital to $6 a^2+11 a-35$, what is the share of each partner?
Sol. Share of each partner $=6 a^2+11 a-35$
$$
\begin{aligned}
& 6 a^2-10 a+21 a-35 \\
& 2 a(3 a-5)+7(3 a-5) \\
& (3 a-5)(2 a+7)
\end{aligned}
$$
Hence share of both brothers $=(3 a-5)$ and $(2 a+7)$
Q. 5. What is the value of each partners share if value of $a=3$ ?
Sol. If value of $a=3$, then share of each partner is
$$
\begin{gathered}
(3 a-5)=(3 \times 3-5)=(9-5)=4 \\
(2 a+7)=(2 \times 3+7)=6+7=13
\end{gathered}
$$
Also check
- Factorisation Class 8 Case Study Questions Maths Chapter 12
- Direct and Inverse Proportions Class 8 Case Study Questions Maths Chapter 11
- Exponents and Powers Class 8 Case Study Questions Maths Chapter 10
- Mensuration Class 8 Case Study Questions Maths Chapter 9
- Algebraic Expressions and Identities Class 8 Case Study Questions Maths Chapter 8
- Comparing Quantities Class 8 Case Study Questions Maths Chapter 7
- Cube and Cube Roots Class 8 Case Study Questions Maths Chapter 6
- Square and Square Roots Class 8 Case Study Questions Maths Chapter 5
- Data Handling Class 8 Case Study Questions Maths Chapter 4
- Understanding Quadrilaterals Class 8 Case Study Questions Maths Chapter 3
- Linear Equations in One Variable Class 8 Case Study Questions Maths Chapter 2
- Rational Numbers Class 8 Case Study Questions Maths Chapter 1
Download eBooks for CBSE Class 8 Maths
- Rational Numbers Topicwise Worksheet for CBSE Class 8 Maths
- Linear Equations in One Variable Worksheet for CBSE Class 8 Maths
- Understanding Quadrilaterals Worksheet for CBSE Class 8 Maths
- Data Handling Worksheet for CBSE Class 8 Maths
- Squares and Square Roots Worksheet for CBSE Class 8 Maths
- Cube and Cube Roots Worksheet for CBSE Class 8 Maths
- Comparing Quantities Worksheet for CBSE Class 8 Maths
- Algebraic Expressions and Identities Worksheet for CBSE Class 8 Maths
Topics from which case study questions may be asked
- Factors of Natural Numbers
- Factors of Algebraic Expressions
- Factorisation – Method of Common Factors
- Factorisation by Regrouping Terms
- Factorisation using Identities
- Factors of form (x+a) (x+b)
- Division of Algebraic Expressions
- Division of a Monomial by another monomial
- Division of a polynomial by a monomial
- Division of Algebraic Expression Continued (Polynomial ÷ Polynomial)
The method by which we find two or more numbers whose product is the given number is called ‘Factorisation’. And these two or more numbers are called ‘factors’ of the given number
e.g., Factors of 6 are = 2 × 3
- All positive integers are natural numbers. And factors of all these Natural Numbers is the product of two or more natural numbers.
- A factor which is divided by 1 and itself are called Prime factors.
Case study questions from the above given topic may be asked.
Frequently Asked Questions (FAQs) on Factorisation Case Study
Q1: What is factorisation?
A1: Factorisation is the process of breaking down a mathematical expression into a product of its factors. These factors can be numbers, variables, or algebraic expressions that, when multiplied together, give the original expression.
Q2: What are the common methods of factorisation?
A2: The common methods of factorisation include:
– Factorisation by taking common factors: Identifying and extracting the greatest common factor (GCF) from the terms.
– Factorisation by grouping terms: Grouping terms to factorise expressions with more than two terms.
– Factorisation of trinomials: Using patterns such as $a^2+2 a b+b^2=(a+b)^2$ or $a^2-b^2=$ $(a-b)(a+b)$
– Factorisation by splitting the middle term: Used in quadratic expressions like $a x^2+b x+c$, where the middle term is split to factor the expression.
Q3: How do you factorise an algebraic expression by taking common factors?
A3: To factorise an expression by taking common factors, you first find the highest common factor (HCF) of all terms in the expression and then factor it out.
Q4: What is factorisation by grouping terms?
A4: Factorisation by grouping is used when an expression has four or more terms. You group terms in pairs (or groups) and factor out the common factors from each group.
Q5: What is the importance of factorisation in mathematics?
A5: Factorisation is important because it simplifies complex algebraic expressions, making them easier to solve or evaluate. It is used in solving quadratic equations, simplifying fractions, and finding roots of polynomials. Factorisation also helps in understanding the structure of algebraic expressions.
Q6: Can you provide an example of inverse proportion in daily life?
A6: A typical example of inverse proportion is the relationship between the number of workers and the time taken to complete a task. If more workers are assigned to a job, the time required to finish the work decreases proportionally, assuming the work is equally distributed among the workers.
Q7: What is the difference between prime factorisation and algebraic factorisation?
A7: Prime factorisation involves breaking down a number into its prime number factors (e.g., $12=$ $2^2 \times 3$ ). Algebraic factorisation, on the other hand, refers to breaking down algebraic expressions into simpler factors (e.g., $x^2-9=(x-3)(x+3)$ ).
Q8: How do you check if factorisation is correct?
A8: To check if factorisation is correct, you can expand the factors (multiply them back together) and see if the result matches the original expression. If they do, the factorisation is correct.
Q9: Are there any online resources or tools available for practicing Direct and Inverse Proportions case study questions?
A9: We provide case study questions for CBSE Class 8 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.
