Find the best tutors and institutes for Class 10 Tuition
Q2(i):
Write the coefficients of $x^2$ in each of the following:
(i) $2 + x^2 + x$
Solution :
Given Variables & Initial Setup
Let the given algebraic expression be denoted as a polynomial function $P(x)$:
$P(x) = 2 + x^2 + x$
Our objective is to determine the coefficient of the $x^2$ term. [A coefficient is defined mathematically as the numerical or constant multiplier of a specific variable within an algebraic term].
Step 1: Standardizing the Polynomial Form
To systematically analyze the polynomial, we first rearrange its terms in descending order of their degree to express it in standard form.
$P(x) = x^2 + x + 2$
[Per the standard convention of polynomial representation, where terms are ordered from the highest exponent to the lowest exponent].
Step 2: Isolating the Target Term
We inspect the standardized polynomial to locate the specific term containing the variable $x$ raised to the power of $2$. The polynomial consists of three distinct terms separated by addition:
- First term: $x^2$ (Quadratic term, Degree 2)
- Second term: $x$ (Linear term, Degree 1)
- Third term: $2$ (Constant term, Degree 0)
The target term for our analysis is $+x^2$.
Step 3: Extracting the Coefficient
We must identify the constant numerical value that multiplies the variable $x^2$. In algebra, when a variable does not have an explicitly written numerical prefix, it is implicitly multiplied by $1$.
$x^2 = 1 \cdot x^2$
[By the Multiplicative Identity Property of Real Numbers, which states that any real number or variable multiplied by $1$ remains unchanged, i.e., $a \cdot 1 = a$].
Therefore, the numerical multiplier (coefficient) of the $x^2$ term is exactly $1$.
Final Solution: The coefficient of $x^2$ in the polynomial $2 + x^2 + x$ is $1$.
More Questions from Class 9 Mathematics Polynomials EXERCISE 2.1
- Q1(i): Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. (i) $4x^2 – 3x + 7$
- Q1(ii): Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. (ii) $y^2 + \sqrt{2}$
- Q1(iii): Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. (iii) $3\sqrt{t} + t\sqrt{2}$
- Q1(iv): Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. (iv) $y + \frac{2}{y}$
- Q1(v): Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. (v) $x^{10} + y^3 + t^{50}$
- Q2(ii): Write the coefficients of $x^2$ in each of the following: (ii) $2 – x^2 + x^3$
- Q2(iii): Write the coefficients of $x^2$ in each of the following: (iii) $\frac{\pi}{2}x^2 + x$
- Q2(iv): Write the coefficients of $x^2$ in each of the following: (iv) $\sqrt{2}x - 1$
- Q3: Give one example each of a binomial of degree 35, and of a monomial of degree 100.
- Q4(i): Write the degree of each of the following polynomials: (i) $5x^3 + 4x^2 + 7x$
- Q4(ii): Write the degree of each of the following polynomials: (ii) $4 – y^2$
- Q4(iii): Write the degree of each of the following polynomials: (iii) $5t – \sqrt{7}$
- Q4(iv): Write the degree of each of the following polynomials: (iv) $3$
- Q5(i): Classify the following as linear, quadratic and cubic polynomials: (i) $x^2 + x$
- Q5(ii): Classify the following as linear, quadratic and cubic polynomials: (ii) $x – x^3$
- Q5(iii): Classify the following as linear, quadratic and cubic polynomials: (iii) $y + y^2 + 4$
- Q5(iv): Classify the following as linear, quadratic and cubic polynomials: (iv) $1 + x$
- Q5(v): Classify the following as linear, quadratic and cubic polynomials: (v) $3t$
- Q5(vi): Classify the following as linear, quadratic and cubic polynomials: (vi) $r^2$
- Q5(vii): Classify the following as linear, quadratic and cubic polynomials: (vii) $7x^3$
CBSE Solutions for Class 9 Mathematics Polynomials
Chapters in CBSE - Class 9 Mathematics
Top Tutors who teach Polynomials
Top Tutor
Nehru Nagar, Belgaum
2 yrs of
Exp
9 students
239 hrs of classes completed
260
per hour
Online Classes
I teach Mathematics to students from Class 7 to Class 10, with 3 years of teaching experience. My focus is on helping students build strong conceptual understanding and develop effective problem-solving skills to excel academically. I have completed my 2nd PUC (Pre-University Course), a Bachelor of Engineering (B.E.) from Visveswaraya Technological University in 2020, and a Bachelor of Education (B.Ed.) from Indira Gandhi National Open University in 2022. I have also completed a program with Cambridge Learning Resources, which has enhanced my teaching techniques and ability to engage students effectively. Over the years, I have guided students to improve their Mathematics understanding and performance, helping them gain confidence in handling both basic and complex problems. My teaching approach emphasizes clarity, practice, and logical reasoning to ensure steady improvement. I have also earned an RPA (Robotic Process Automation) certification in robotics, which reflects my technical skills and commitment to continuous learning. I often incorporate logical thinking and problem-solving strategies inspired by this training into my lessons. I prefer to conduct online classes, offering flexibility in timing and easy access for students. I teach both individual and small group sessions, allowing personalized attention and interactive learning experiences for every student. My classes are interactive, using motivational videos, personal digital pads, and other digital tools to make learning engaging and effective. These resources help students visualize concepts better and retain knowledge more efficiently. I provide custom-prepared notes to support student learning and revision. My ultimate goal is to make Mathematics understandable, enjoyable, and confidence-building, enabling every student to perform at their best and develop a strong foundation for future studies.
This guy is too good at his teaching. He explains the concepts very clear, gets to know about the students, gives his own ideas, own methods, and also gives good advices. He is excellent to consider. I just like him!, he is a great tutor and price is reasonably good.
Top Tutor
Alamganj, Patna
4 yrs of
Exp
9 students
16 hrs of classes completed
200
per hour
Student's Home
Tutor's home
I am teaching in school ( Dalimss Sunbeam school Ghazipur ) as a PGT teacher.. I have over all 4 years experience in this field.
Super Tutor
Saheed Nagar, Bhubaneswar
11 yrs of
Exp
32 students
601 hrs of classes completed
599
per hour
Online Classes
▪️Class 10 Board Specialist ▪️IGCSE / IB / CBSE / ICSE / Focus ▪️Syllabus-Aligned Teaching ▪️Concept Clarity First ▪️Exam-Oriented Preparation ▪️Board Pattern Mastery ▪️Previous Year Questions Practice ▪️Structured Lesson Planning ▪️Step-by-Step Problem Solving ▪️Time Management Training ▪️Weekly Tests & Mock Exams ▪️Performance Tracking ▪️Targeted Weak Area Support ▪️Answer Writing Techniques ▪️Regular Parent Updates ▪️Result-Driven Approach
Very interactive. The way sir explained with otes and figures are very eazy to understand. I am sure i will learn a lot from sir.
Top Tutor
West Marredpally, Hyderabad
20 yrs of
Exp
92 hrs of classes completed
400
per hour
Online Classes
Student's Home
Tutor's home
I have more than 15 years teaching experience in teaching CBSE classes 8-10 Physics/Chemistry. I can also teach math upto 9th . All my students secured 10/10 in previous years exams. And in school more than 90% students got more than 90 in Science Exam and all have passed in Science i. Physics and Chemistry.
Top Tutor
SCB Nagar, Kothagudem
20 yrs of
Exp
32 students
2183 hrs of classes completed
450
per hour
Online Classes
22 Years Experience in Schools IN ICSE/CBSE/IGCSE IN DIFFERENT STATE BOARDS
Sir is very friendly teacher he will support us more he is the best teacher of the year his teaching skills are really good.
Find more Tutor for Polynomials in your City
- Bangalore Mathematics Tutors
- Delhi Mathematics Tutors
- Chennai Mathematics Tutors
- Gurgaon Mathematics Tutors
- Noida Mathematics Tutors
- Hyderabad Mathematics Tutors
- Mumbai Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Chandigarh Mathematics Tutors
- Pune Mathematics Tutors
- Jaipur Mathematics Tutors
- Surat Mathematics Tutors
