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(ii):
Write the coefficients of $x^2$ in each of the following: (ii) $2 – x^2 + x^3$

Solution :

Given Polynomial & Initial Setup

We are given the algebraic expression:

$P(x) = 2 - x^2 + x^3$

Our objective is to determine the numerical coefficient of the $x^2$ term within this polynomial.

Step 1: Understanding Polynomial Terms and Standard Form

[Per the algebraic definition of a polynomial], an expression is composed of distinct terms separated by addition ($+$) or subtraction ($-$) operators. To analyze the polynomial systematically, it is best practice to rewrite it in standard form, where the terms are ordered by descending powers of the variable $x$.

Rearranging $P(x)$ yields:

$P(x) = x^3 - x^2 + 2$

Step 2: Isolating the Target Term

We must identify the specific term that contains the variable $x^2$. By dissecting the polynomial into its constituent terms, we get:

  • Cubic term: $+x^3$
  • Quadratic term: $-x^2$
  • Constant term: $+2$

The target term containing $x^2$ is explicitly $-x^2$.

Step 3: Extracting the Numerical Coefficient

[By the fundamental axioms of algebra], the coefficient is the constant multiplicative factor attached to a variable in a specific term. When a variable appears without an explicit numerical multiplier but carries a negative sign, the multiplicative identity property dictates that the hidden multiplier is $-1$.

We can expand the target term algebraically to reveal its coefficient:

$-x^2 = (-1) \cdot x^2$

Thus, the numerical factor multiplying $x^2$ is $-1$.

Visual Breakdown of the Polynomial Terms

2 Constant -x² Target Term +x³ Cubic Term (-1) · x² Coefficient = -1

Final Solution: The coefficient of $x^2$ in the polynomial $2 - x^2 + x^3$ 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

(203)
Top Tutor
locationImg Venkatraman Nagar Chennai, Chennai
experience 10 yrs of Exp students 27 students
greenClock 3790 hrs of classes completed
rsIcon 320 per hour
Expereinced Tutor for class 9- class 12 on maths and sxience subjects
Online Classes Online Classes
regularClasses Tutor's home

im having good experince in teaching with make them understand the concepts better

Amudha

Classes are much interactive so useful to assess the students understanding capacity during the class itself.

Skills: Mathematics , Science
Also teaches: Class 12 Tuition, Class 11 Tuition and more

locationImg Govindpuram, Ghaziabad
experience 20 yrs of Exp students 1 student
greenClock 34 hrs of classes completed
Maths teacher for last 15 years
Online Classes Online Classes
homeTutions Student's Home
regularClasses Tutor's home

I teach mathematics and science for class 10th students. In science I teach physics chemistry and biology. My aim is to teach the students in way so that they score 100percent in boards.

Skills: Mathematics , Science
Also teaches: Class 11 Tuition, Class 8 Tuition and more

(22)
Top Tutor
locationImg Bicholi Mardana Neer Nagar, Indore
experience 8 yrs of Exp students 12 students
greenClock 362 hrs of classes completed
rsIcon 900 per hour
M.Sc(Mathematics) and B.Ed with 14 years of experience in CBSE and ICSE boards.
Online Classes Online Classes

I have Taught 3 years in CBSE board and 5 years In ICSE board in class 10 with 100% results.Got an opportunity to go for CBSE board class 10 Maths copy correction.Was Board examiner head for ICSE .

Aparna Agarwal

Pragya ma'am is amazing! She helped me with maths a lot! Great teacher!

Skills: Mathematics , Physics

(7)
Top Tutor
locationImg Indirapuram, Ghaziabad
experience 5 yrs of Exp
greenClock 39 hrs of classes completed
Online Tutor Available for Every Student
Online Classes Online Classes

I was a working professional .Left my job and started teaching as a tutor. I have been a national level debater . I am a famous teacher amongst my students .

Skills: English , Mathematics and more
Also teaches: Selenium, Sanskrit Language and more

(98)
Top Tutor
locationImg Thane West, Thane
experience 20 yrs of Exp students 37 students
greenClock 5543 hrs of classes completed
rsIcon 350 per hour
I love to teach from the basics.
Online Classes Online Classes

This is Prita Chatterjee with 27 years of teaching in the Engineering College and Schools .I teach Maths for all the boards - IB AA(SL& HL) ,IB - AI(HL&SL),Integrated Maths ,MYP ,Cambridge A Level , Additional Maths, IGCSE O Level, ISC, ICSE , CBSE .Presently, I am tutoring students from U.S. France, Austrailia , Netherland , Japan, Singapore, Malaysia , Thailand , Phillipines , Dubai , Riyadh , Doha, and pan India . I would love to teach from basics . .If you would like me to teach your child , kindly let me know ,so we can schedule a demo ,as per suitability.

Sandeep Kumar

She is a good teacher with very well and skilled explanations and making sure that students do each and every sum from text book.Hoping that she teaches out of the book&concepts too.:) my only concern is I can’t expect the reply for my messages as quick.

Skills: Mathematics
Also teaches: Class 7 Tuition, Class 9 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 »