default_background
✕

Find the best tutors and institutes for Class 10 Tuition

Find Best Class 10 Tuition

Please select a Category.

Please select a Locality.

No matching category found.

No matching Locality found.

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 $1$.


Term: x² 1 · x² Coefficient 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


CBSE Solutions for Class 9 Mathematics Polynomials


Chapters in CBSE - Class 9 Mathematics


Top Tutors who teach Polynomials

Gerard Antony Class 10 Tuition trainer in Mira-Bhayandar
(10)
Top Tutor
locationImg Mira Road, Mira-Bhayandar
experience 10 yrs of Exp students 7 students
greenClock 84 hrs of classes completed
rsIcon 600 per hour
MATH, SCIENCE Teacher with 10 years of experience.
homeTutions Student's Home
regularClasses Tutor's home

Math and physics teacher. Expert in cbse education and assessment patten. Been an cbse examiner for 5 continuous years. Aware of the curriculum of ssc, icse and cbse grade 7-10 math and physics. Tutoring since 2006 and been quite successful in giving results.

Anas Khan

I would like to say the class was really helpful. I was able to catch a hold on various topics taught in class. Sir also has a very kind nature and he helped us in various way. Overall I loved the class.

Skills: Mathematics , Science
Also teaches: B Ed Tuition, Class 8 Tuition and more

Saurav Class 10 Tuition trainer in Mumbai
(25)
Top Tutor
locationImg Nerul, Mumbai
experience 10 yrs of Exp students 5 students
greenClock 640 hrs of classes completed
rsIcon 450 per hour
M.SC MATHS from JAMIA MILLIA ISLAMIA, NEW DELHI, 10+Years of Teaching Experience.
Online Classes Online Classes
homeTutions Student's Home
regularClasses Tutor's home

I have specifically guided Class 10 students for board exams, with a strong focus on NCERT syllabus, and topics like Real Numbers, Polynomials, Quadratic Equations, and Statistics. I provide regular tests, personalized feedback, and exam-oriented strategies to improve accuracy and speed. Many of my students have shown remarkable improvement and scored above 90% in their board exams.

Vivek Yadav

It was an amazing experience learning and understanding maths with Saurav sir. He really helped me overcome my fear of maths and helped me score good marks in a subject that previously scared me. It really shows how dedicated he is as a teacher. Really good experience!

Skills: Mathematics
Also teaches: Class 9 Tuition, Class 8 Tuition and more

(9)
Top Tutor
locationImg Sonari, Jamshedpur
experience 1 yrs of Exp students 4 students
greenClock 657 hrs of classes completed
rsIcon 300 per hour
Online Classes Online Classes
homeTutions Student's Home
regularClasses Tutor's home

I have a Science background completed my electrical engineering.... I am giving home tuition for 2 years.... I am also preparing for UPSC civil service exam.

Dipali Nagila

Wonderful experience part one month. Look forward to taking more classes with sir. Like the dedicated teaching style.

Skills: Mathematics , Physics and more
Also teaches: Class 9 Tuition, Class 8 Tuition and more

(35)
Top Tutor
locationImg Sector-16, Faridabad
experience 1 yrs of Exp students 4 students
greenClock 532 hrs of classes completed
rsIcon 400 per hour
PROFESSIONAL TUTOR FROM BITS PILANI
Online Classes Online Classes
homeTutions Student's Home
regularClasses Tutor's home

I have taught my two sons when they were in class 10. They manged to clear the IIT JEE exam in 1st attempt. I teach by example, which helps the students to visualize the concepts and ideas. I believe in participative learning where the student also gives their viewpoints. This is how they start enjoying the subject and their performance level increases automatically.

Hemanshi

My experience so far is great with Sir. He teaches topics very well. He also focuses on the practical applications of the topics.

Skills: Mathematics , Information and Comunication Technology and more
Also teaches: HTML, Python Training and more

locationImg Carterpuri, Palam Vihar, Gurgaon
experience 20 yrs of Exp
rsIcon 500 per hour
Learning forever
homeTutions Student's Home

I am a professional teacher with more than 25 years of teaching experience in prestigious schools of India.My teaching assures value for money and produce best results.I emphasize on concepts clarity and create natural interest in the subject.

Skills: Mathematics , Physics and more
Also teaches: Class 6 Tuition, Class 12 Tuition and more

Find more Tutor for Polynomials in your City


Other Subjects in CBSE - Class 9

Worksheet Icon

Download free CBSE - Class 9 Mathematics Polynomials EXERCISE 2.1 worksheets

Download Now

Find Best Class 10 Tuition ?

Find Now »