Find the best tutors and institutes for Class 10 Tuition
Q5(iii):
Classify the following as linear, quadratic and cubic polynomials:
(iii) $y + y^2 + 4$
Solution :
Initial Setup & Given Expression
We are tasked with classifying the following algebraic expression based on its degree:
$P(y) = y + y^2 + 4$
Step 1: Rearranging into Standard Form
By mathematical convention, polynomials are typically written in standard form, where the terms are ordered from the highest power of the variable to the lowest power [Descending Order of Exponents]. This makes it easier to identify the leading term and the degree.
Rearranging the terms of $P(y)$ according to the powers of $y$:
$P(y) = y^2 + y + 4$
Step 2: Analyzing the Exponents of Each Term
To classify the polynomial, we must determine the exponent of the variable $y$ in each distinct term. We apply the fundamental laws of exponents to reveal hidden powers:
- First term ($y^2$): The exponent of the variable $y$ is explicitly $2$.
- Second term ($y$): Any variable written without an explicit exponent has an implied exponent of $1$. Thus, $y = y^1$. The exponent is $1$.
- Third term ($4$): This is a constant term. By the zero exponent rule [where $y^0 = 1$ for $y \neq 0$], a constant $c$ can be written as $c \cdot y^0$. Therefore, $4 = 4y^0$. The exponent of $y$ here is $0$.
Step 3: Determining the Degree of the Polynomial
The degree of a polynomial in one variable is defined as the highest power (maximum exponent) of the variable present in the expression, provided its coefficient is non-zero.
Comparing the set of exponents we identified $\{2, 1, 0\}$, the maximum value is $2$.
Therefore, the degree of the polynomial $P(y)$ is $2$.
Step 4: Classification Based on Degree
In algebraic nomenclature, polynomials are classified strictly according to their degree. The standard classifications are outlined in the table below:
| Degree | Polynomial Classification | General Form (in variable $x$) |
|---|---|---|
| 1 | Linear | $ax + b \quad (a \neq 0)$ |
| 2 | Quadratic | $ax^2 + bx + c \quad (a \neq 0)$ |
| 3 | Cubic | $ax^3 + bx^2 + cx + d \quad (a \neq 0)$ |
Because the highest exponent of the variable $y$ in the expression $y^2 + y + 4$ is exactly $2$, it perfectly matches the definition of a quadratic polynomial.
Final Solution
Final Solution: The given polynomial $y + y^2 + 4$ has a degree of 2, and is therefore classified as a quadratic polynomial.
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(i): Write the coefficients of $x^2$ in each of the following: (i) $2 + x^2 + x$
- 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(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
Super Tutor
Badarpur, Delhi
11 yrs of
Exp
145 students
3604 hrs of classes completed
200
per hour
Online Classes
Tutor's home
I am utterly grateful to Akshay sir for his unending support and sincere guidance. He was such a big pillar of support in my board exams and his style of teaching is truly exceptional!!!! His notes, his previous year questions, his tips and his advices are really helpful for the board exams. I was able to score 97.2% in my boards because of his style of teaching. In fact all the topics he marked as important came in the board exams! Moreover he is a very hardworking and dedicated teacher with an unending passion to support and tutor children. I really am grateful to you Akshay sir Regards Nirvaan Rai Batch 2025-26
Super Tutor
Kodambakkam, Chennai
15 yrs of
Exp
57 students
3744 hrs of classes completed
800
per hour
Online Classes
With a decade of experience in teaching mathematics, physics, and chemistry for students from grades 8 through 12 across CBSE, IB, and ICSE boards, I offer a comprehensive educational approach that caters to a diverse range of curricula and learning needs. My academic background includes a BE and an MBA, equipping me with both technical and managerial skills that enhance my teaching methodology. Throughout my career, I have specialized in home tutoring, where I have developed a personalized approach to education that focuses on each student's unique needs and strengths. My sessions are designed to be interactive and engaging, fostering a learning environment where students feel supported and motivated. I conduct both online and offline classes, each lasting one hour, and utilize a variety of teaching tools to facilitate learning. I employ a whiteboard to visually explain concepts and provide question papers to help students practice and prepare for their exams. This hands-on approach ensures that students not only understand theoretical concepts but also develop problem-solving skills and confidence in their subjects. My commitment to delivering high-quality education and my extensive experience make me well-suited to guide students through their academic journey, helping them achieve their full potential in mathematics, physics, and chemistry.
Super Tutor
Nerul Sector 20, Thane
10 yrs of
Exp
62 students
2804 hrs of classes completed
1200
per hour
Online Classes
I have done b.Tech in electrical engineering from IIT KANPUR. I taught one year in akash institute patna, 2 years in fiitjee patna. Currently I am teaching in unacademy. I have taught more than 6000 jee and neet aspirants. In which more than 500 students are selected in iitand aiims. If some one is interested to improve their physics upto jee advanced level take help with me .And see the magic. I can help students in their all type of assignment from any institute like allen, fiitjee, narayna, akash, resonance. I can help students to solve both volume of h.C verma within two month if some one is intrested in solving I.E.Irodov join me and see the next level of physics. My way of teaching is so easy and so advanced that student will realyy enjoy it. Don't waste your time in making decision just join and experience my level
He is a very dedicated teacher with excellent knowledge on topic. He knows Subject very well and teach accordingly to kids.
Super Tutor
Basaveshwara Nagar, Bangalore
12 yrs of
Exp
12 students
3331 hrs of classes completed
600
per hour
Online Classes
With over 15 years of dedicated teaching experience, I am an accomplished and qualified educator specializing in Spoken English, Math, Science, Social Science, and Kannada Language. My expertise extends across various educational boards, including CBSE, ICSE, and state boards. Passionate about unraveling the mysteries of mathematical problems and chemical equations. I have garnered recognition with the prestigious Best Teacher Award for orchestrating state-level Science exams. Having contributed my skills to the esteemed MaxMuller Public School in Bangalore, I am committed to fostering a nurturing and inspiring learning environment. Join me on this educational journey where knowledge meets enthusiasm!
Enrolled my 10-year-old for math tutoring, and the improvement is remarkable. The tutor identifies weak spots quickly, like multiplication tables. Fun drills with timers make practice competitive and enjoyable. She explains errors without blame, turning mistakes into lessons. Custom worksheets align with his CBSE curriculum spot-on. Confidence boost evident; he volunteers answers in class now. Test scores rose steadily over two months. Responsive to parent queries, even on weekends. Affordable rates for such quality one-on-one attention. Planning long-term enrollment—excellent choice!
Super Tutor
Katira Maharaja Hata, Arrah
4 yrs of
Exp
24 students
1771 hrs of classes completed
700
per hour
Online Classes
Tutor's home
I've been teaching Class 10th students of schools from India and abroad. I primarily work with them to prepare for Olympiad, JEE foundation and school exams. I've been teaching students of class 8th-10th Science and Mathematics for more than 3 years. So far, I have taught more than 100 students from India and abroad. I teach international students Mathematics, Physics and Chemistry. I teach almost all boards of India such as CBSE, ICSE and state boards. I also teach IGCSE and IB students. I've my offline coaching institute where I am teaching students of CBSE and state boards who require help in Science and Mathematics. Fee displayed on my profile is for 1Ă—1 classes. For group classes, the fee is substantially reduced.
Find more Tutor for Polynomials in your City
- Delhi Mathematics Tutors
- Bangalore Mathematics Tutors
- Hyderabad Mathematics Tutors
- Chennai Mathematics Tutors
- Kolkata Mathematics Tutors
- Mumbai Mathematics Tutors
- Noida Mathematics Tutors
- Pune Mathematics Tutors
- Gurgaon Mathematics Tutors
- Lucknow Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Jaipur Mathematics Tutors
