Maharashtra Board Solutions Class 9-Maths (Part 1): Chapter 3.1- Polynomials
Maharashtra Board Solutions Class 9-Maths (Part 1): Chapter 3.1- Polynomials

Class 9: Maths Chapter 3.1 solutions. Complete Class 9 Maths Chapter 3.1 Notes.

Maharashtra Board Solutions Class 9-Maths (Part 1): Chapter 3.1- Polynomials

Maharashtra Board 9th Maths Chapter 3.1, Class 9 Maths Chapter 3.1 solutions

Question 1.
State whether the given algebraic expressions are polynomials? Justify.
i. y + 1y
ii. 2 – 5√x
iii. x2 + 7x + 9
iv. 2m-2 + 7m – 5
v. 10
Answer:
i. No, because power of v in the term 5√x is -1 (negative number).
ii. No, because the power of x in the term 5√x is
i. e. 0.5 (decimal number).
iii. Yes. All the coefficients are real numbers. Also, the power of each term is a whole number.
iv. No, because the power of m in the term 2m-2 is -2 (negative number).
v. Yes, because 10 is a constant polynomial.

Question 2.
Write the coefficient of m3 in each of the given polynomial.
i. m3
ii. 2–√−3 + m – √3m3
iii. 3–√−2m3 + 5m2 – 7m -1
Answer:
i. 1
ii. -√3
iii. – 23

Question 3.
Write the polynomial in x using the given information. [1 Mark each]
i. Monomial with degree 7
ii. Binomial with degree 35
iii. Trinomial with degree 8
Answer:
i. 5x7
ii. x35 – 1
iii. 3x8 + 2x6 + x5

Question 4.
Write the degree of the given polynomials.
i. √5
ii. x°
iii. x2
iv. √2m10 – 7
v. 2p – √7
vi. 7y – y3 + y5
vii. xyz +xy-z
viii. m3n7 – 3m5n + mn
Answer:
i. √5 = √5 x°
∴ Degree of the polynomial = 0

ii. x°
∴Degree of the polynomial = 0

iii. x2
∴Degree of the polynomial = 2

iv. √2m10 – 7
Here, the highest power of m is 10.
∴Degree of the polynomial = 10

v. 2p – √7
Here, the highest power of p is 1.
∴ Degree of the polynomial = 1

vi. 7y – y3 + y5
Here, the highest power of y is 5.
∴Degree of the polynomial = 5

vii. xyz + xy – z
Here, the sum of the powers of x, y and z in the term xyz is 1 + 1 + 1= 3,
which is the highest sum of powers in the given polynomial.
∴Degree of the polynomial = 3

viii. m3n7 – 3m5n + mn
Here, the sum of the powers of m and n in the term m3n7 is 3 + 7 = 10,
which is the highest sum of powers in the given polynomial.
∴ Degree of the polynomial = 10

Question 5.
Classify the following polynomials as linear, quadratic and cubic polynomial. [2 Marks]
i. 2x2 + 3x +1
ii. 5p
iii. √2 – 12
iv. m3 + 7m2 + 2–√5m – √7
v. a2
vi. 3r3
Answer:
Linear polynomials: ii, iii
Quadratic polynomials: i, v
Cubic polynomials: iv, vi

Question 6.
Write the following polynomials in standard form.
i. m3 + 3 + 5m
ii. – 7y + y5 + 3y3 – 12+ 2y4 – y2
Answer:
i. m3 + 5m + 3
ii. y5 + 2y4 + 3y3 – y2 – 7y – 12

Question 7.
Write the following polynomials in coefficient form.
i. x3 – 2
ii. 5y
iii. 2m4 – 3m2 + 7
iv. – 23
Answer:
i. x3 – 2 = x3 + 0x2 + 0x – 2
∴ Coefficient form of the given polynomial = (1, 0, 0, -2)

ii. 5y = 5y + 0
∴Coefficient form of the given polynomial = (5,0)

iii. 2m4 – 3m2 + 7
= 2m4 + Om3 – 3m2 + 0m + 7
∴ Coefficient form of the given polynomial = (2, 0, -3, 0, 7)

iv. – 23
∴Coefficient form of the given polynomial = (- 23)

Question 8.
Write the polynomials in index form.
i. (1, 2, 3)
ii. (5, 0, 0, 0 ,-1)
iii. (-2, 2, -2, 2)
Answer:
i. Number of coefficients = 3
∴ Degree = 3 – 1 = 2
∴ Taking x as variable, the index form is x2 + 2x + 3

ii. Number of coefficients = 5
∴ Degree = 5 – 1=4
∴ Taking x as variable, the index form is 5x4 + 0x3 + 0x2 + 0x – 1

iii. Number of coefficients = 4
∴Degree = 4 – 1 = 3
∴Taking x as variable, the index form is -2x3 + 2x2 – 2x + 2

Question 9.
Write the appropriate polynomials in the boxes.
Maharashtra Board Class 9 Maths Solutions Chapter 3 Polynomials Practice Set 3.1 1
Answer:
i. Quadratic polynomial: x2; 2x2 + 5x + 10; 3x2 + 5x
ii. Cubic polynomial: x3 + x2 + x + 5; x3 + 9
iii. Linear polynomial: x + 7
iv. Binomial: x + 7; x3 + 9; 3x2 + 5x
v. Trinomial: 2x2 + 5x + 10
vi. Monomial: x2

Question 1.
Write an example of a monomial, a binomial and a trinomial having variable x and degree 5. ( Textbook pg. no. 3)
Answer:
Monomial: x5
Binomial: x5 + x
Trinomial: 2x5 – x2 + 5

Question 2.
Give example of a binomial in two variables having degree 5. (Textbook pg. no. 38)
Answer:
x3y2 + xy

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Maharashtra Board Solutions Class 9-Maths (Part 1): Chapter 3.1- Polynomials

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Chapterwise Maharashtra Board Solutions Class 9 Maths :

Part 1

FAQs

Where do I get the Maharashtra State Board Books PDF For free download?

You can download the Maharashtra State Board Books from the eBalbharti official website, i.e. cart.ebalbharati.in or from this article.

How to Download Maharashtra State Board Books?

Students can get the Maharashtra Books for primary, secondary, and senior secondary classes from here.  You can view or download the Maharashtra State Board Books from this page or from the official website for free of cost. Students can follow the detailed steps below to visit the official website and download the e-books for all subjects or a specific subject in different mediums.
Step 1: Visit the official website ebalbharati.in
Step 2: On the top of the screen, select “Download PDF textbooks” 
Step 3: From the “Classes” section, select your class.
Step 4: From “Medium”, select the medium suitable to you.
Step 5: All Maharashtra board books for your class will now be displayed on the right side. 
Step 6: Click on the “Download” option to download the PDF book.

Who developed the Maharashtra State board books?

As of now, the MSCERT and Balbharti are responsible for the syllabus and textbooks of Classes 1 to 8, while Classes 9 and 10 are under the Maharashtra State Board of Secondary and Higher Secondary Education (MSBSHSE).

How many state boards are there in Maharashtra?

The Maharashtra State Board of Secondary & Higher Secondary Education, conducts the HSC and SSC Examinations in the state of Maharashtra through its nine Divisional Boards located at Pune, Mumbai, Aurangabad, Nasik, Kolhapur, Amravati, Latur, Nagpur and Ratnagiri.

About Maharashtra State Board (MSBSHSE)

The Maharashtra State Board of Secondary and Higher Secondary Education or MSBSHSE (Marathi: महाराष्ट्र राज्य माध्यमिक आणि उच्च माध्यमिक शिक्षण मंडळ), is an autonomous and statutory body established in 1965. The board was amended in the year 1977 under the provisions of the Maharashtra Act No. 41 of 1965.

The Maharashtra State Board of Secondary & Higher Secondary Education (MSBSHSE), Pune is an independent body of the Maharashtra Government. There are more than 1.4 million students that appear in the examination every year. The Maha State Board conducts the board examination twice a year. This board conducts the examination for SSC and HSC. 

The Maharashtra government established the Maharashtra State Bureau of Textbook Production and Curriculum Research, also commonly referred to as Ebalbharati, in 1967 to take up the responsibility of providing quality textbooks to students from all classes studying under the Maharashtra State Board. MSBHSE prepares and updates the curriculum to provide holistic development for students. It is designed to tackle the difficulty in understanding the concepts with simple language with simple illustrations. Every year around 10 lakh students are enrolled in schools that are affiliated with the Maharashtra State Board.