Polynomials Class 9 Case Study Questions Maths Chapter 2

Q: Q8: What are the important keywords for CBSE Class 9 Maths Polynomials?

A8: List of important keywords given below - Algebraic Expression: Any expression that contains constants and variables, connected by some or all of the operations +, -, x, ÷. Polynomials: An algebraic expression in which the variables involved have only non-negative integral powers. Polynomials in one Variable: An algebraic expression which consist of only one type of variables in the entire expression. Degree of Polynomial: Highest power of a variable in the polynomial. Constant Polynomial: Polynomial of zero degree. Zero Polynomials: A polynomial consisting of one term, namely zero. Zeroes of a Polynomial: Let p(x) be a polynomial in one variable and 'a' be a real number such that the value of polynomial at x=a is zero i.e., p(a) = 0, then 'a' is said to be a zero polynomial of p(x). Remainder Theorem: Let p(x) be a polynomial having degree 1 or more than 1 and let 'a' be any real number. If p(x) is divided by (x-a), then remainder is p(a).

Download CBSE and ICSE Books in PDF Format

Reading Time: 8 minutes

Last Updated on October 26, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 9 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 9 maths. In this article, you will find case study questions for CBSE Class 9 Maths Chapter 2 Polynomials. It is a part of Case Study Questions for CBSE Class 9 Maths Series.

Chapter	Polynomials
Type of Questions	Case Study Questions
Nature of Questions	Competency Based Questions
Board	CBSE
Class	9
Subject	Maths
Useful for	Class 9 Studying Students
Answers provided	Yes
Difficulty level	Mentioned
Important Link	Class 9 Maths Chapterwise Case Study

Customised Study Materials for Teachers, Schools and Coaching Institute

Table of Contents

Case Study Questions on Polynomials

Questions

In the current scenario, people use such door whose top half part is made of glass and bottom half part is wooden.

The glass portion of the door is having length and width in the ratio of 5 : 3. The wooden frame around the glass portion adds 11 inches to the total width and 14 inches to the total length. Consider the length of the glass portion as 5x inches:

On the basis of the above information, solve the following questions:

Q. 1. Find the total length of the glass portion of the door (in inches) is represented in terms of x.

Q. 2. Find the total width of the glass portion of the door (in inches).

Q. 3. Write the polynomial representation of the area top half part of the door.

Q. 4. Find the zeroes of the polynomial representing the area.

1. The total length of the glass portion in the door is represented by $(5 x+14)$ inches.
2. The total width of the glass portion in the door is $(3 x+11)$ inches.
3. The area of top half part of the door
$$
\begin{aligned}
& =\text { length } \times \text { width } \\
& =(5 x+14)(3 x+11) \\
=& 15 x^2+55 x+42 x+154 \\
& =15 x^2+97 x+154
\end{aligned}
$$
4. We have area, $p(x)=(5 x+14)(3 x+11)$
For finding zeroes, put $p(x)=0$
\begin{array}{ll}
\therefore(5 x+14) (3 x+11)=0 \\
\Rightarrow (5 x+14)=0 \text { or }(3 x+11)=0 \\
\Rightarrow x=\frac{-14}{5} \text { or } x=\frac{-11}{3}
\end{array}

Algebraic Identities

Algebraic equations that are true for all values of variables occurring in it.
Some useful algebraic identities are:

(i) $(x+y)^2=x^2+2 x y+y^2$
(ii) $(x-y)^2=x^2-2 x y+y^2$
(iii) $x^2-y^2=(x+y)(x-y)$
(iv) $(x+a)(x+b)=x^2+(a+b) x+a b$
(v) $(x+y+z)^2$
=$x^2+y^2+z^2+2 x y+2 y z+2 z x$
(vi) $(x+y)^3$
=$x^3+y^3+3 x y(x+y)$
=$x^3+y^3+3 x^2 y+3 x y^2$
(vii) $(x-y)^3$
=$x^3-y^3-3 x y(x-y)$
=$x^3-y^3-3 x^2 y+3 x y^2$
(viii) $x^3+y^3$
=$(x+y)\left(x^2-x y+y^2\right)$
=$(x+y)^3-3 x y(x+y)$
(ix) $x^3-y^3$
=$(x-y)\left(x^2+x y+y^2\right)$
=$(x-y)^3+3 x y(x-y)$
(x) $\left(x^3+y^3+z^3-3 x y z\right)$
$=\left(x+y+z)(x^2+y^2+z^2-x y-y z-z x\right)$
Note:
If $x+y+z=0$, then $x^3+y^3+z^3=3 x y z$

Also check

Topics from which case study questions may be asked

Definition of a polynomial in one variable, with examples and counter examples.
Coefficients of a polynomial
Terms of a polynomial and zero polynomial.
Degree of a polynomial.
Constant, linear, quadratic and cubic polynomials.
Monomials, binomials, trinomials.
Factors and multiples.
Zeros of a polynomial.
Remainder Theorem with examples.

Linear polynomial can be monomial or binomial.

Quadratic polynomial can be monomial, binomial or trinomial.

The degree of a zero polynomial is not defined.

Case study questions from the above given topic may be asked.

Helpful Links for CBSE Class 9 Preparation

Download Customised White Label Study Materials in MS Word Format

We are providing teaching resources to teachers and coaching institute looking for customised study materials in MS word format. Our High-quality editable study material which is prepared by the expert faculties are Highly useful for Teachers, Mentors, Tutors, Faculties, Coaching Institutes, Coaching Experts, Tuition Centers.

Download Product Brochure

Frequently Asked Questions (FAQs) on Polynomials Case Study

Q1: What are polynomials in mathematics?

A1: Polynomials are algebraic expressions that consist of variables and coefficients, connected by addition, subtraction, and multiplication. They can have multiple terms, and the degree of a polynomial is determined by the highest power of the variable in the expression.

Q2: How many types of polynomials are there?

A2: Polynomials are classified based on the number of terms they have:
Monomial: A polynomial with just one term.
Binomial: A polynomial with two terms.
Trinomial: A polynomial with three terms
Multinomial: A polynomial with more than three terms

Q3: What is the degree of a polynomial?

A3: The degree of a polynomial is the highest power of the variable in the polynomial.

Q4: What are the key concepts covered in Chapter 2 of CBSE Class 9 Maths regarding polynomials?

A4: Chapter 2 of CBSE Class 9 Maths covers concepts such as understanding polynomials and its types.
(i) Types of polynomials
(ii) Terms and coefficient of polynomials
(iii) Zeroes of a polynomial
(iv) Division algorithm
(v) Remainder theorem
(vi) Factor theorem
(vii) Factorisation of quadratic polynomial

Q5: What is the difference between a polynomial and a non-polynomial expression?

A5: A polynomial expression consists of variables with non-negative integer exponents and real coefficients, combined using addition, subtraction, and multiplication. Non-polynomial expressions may include variables with negative exponents, fractional exponents, or other operations like division by variables or roots

Q6: What are the common mistakes to avoid when working with polynomials?

A6: Common mistakes include:
Misidentifying the degree of the polynomial.
Incorrectly applying the distributive property when multiplying polynomials.
Forgetting to arrange the polynomial terms in standard form (descending order of exponents).
Overlooking the signs while combining like terms.
Misapplying the rules of exponents.

Q7: Are there any online resources or tools available for practicing polynomials case study questions?

A7: We provide case study questions for CBSE Class 9 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.

Q8: What are the important keywords for CBSE Class 9 Maths Polynomials?

A8: List of important keywords given below –
Algebraic Expression: Any expression that contains constants and variables, connected by some or all of the operations +, -, x, ÷.
Polynomials: An algebraic expression in which the variables involved have only non-negative integral powers.
Polynomials in one Variable: An algebraic expression which consist of only one type of variables in the entire expression.
Degree of Polynomial: Highest power of a variable in the polynomial.
Constant Polynomial: Polynomial of zero degree.
Zero Polynomials: A polynomial consisting of one term, namely zero.
Zeroes of a Polynomial: Let p(x) be a polynomial in one variable and ‘a’ be a real number such that the value of polynomial at x=a is zero i.e., p(a) = 0, then ‘a’ is said to be a zero polynomial of p(x).
Remainder Theorem: Let p(x) be a polynomial having degree 1 or more than 1 and let ‘a’ be any real number. If p(x) is divided by (x-a), then remainder is p(a).