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Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra chapter 3 - Polynomials [Latest edition]

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Maharashtra state board Class 9 Mathematics 1 Algebra - Shaalaa.com

Chapter 3: Polynomials

Practice Set 3.1Practicr Set 3.1Practice Set 3.2Practice Set 3.3Practice Set 3.4Practice Set 3.5Practice Set 3.6Problem Set 3

Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra Chapter 3 Polynomials Exercise Practice Set 3.1, Practicr Set 3.1 [Pages 39 - 40]

Practice Set 3.1 | Q 1.1 | Page 39

State whether the given algebraic expression are polynomial? Justify.

`y + 1/y`

Practice Set 3.1 | Q 1.2 | Page 39

State whether the given algebraic expression are polynomial? Justify.

`2 - 5 sqrt x`

Practice Set 3.1 | Q 1.3 | Page 39

State whether the given algebraic expression are polynomial? Justify.

`x^2 + 7x + 9`

Practice Set 3.1 | Q 1.4 | Page 39

State Whether the Given Algebraic Expression Are Polynomial? Justify.

`2m^(-2) + 7m - 5`

Practice Set 3.1 | Q 1.5 | Page 39

State whether the given algebraic expression are polynomial? Justify.

10

Practice Set 3.1 | Q 2.1 | Page 39

Write the coefficient of m3 in the given polynomial.

`m^3`

Practice Set 3.1 | Q 2.2 | Page 39

Write the coefficient of m3 in the given polynomial.

`-3/2+m - sqrt 3 m^3`

Practice Set 3.1 | Q 2.3 | Page 39

Write the coefficient of m3 in the given polynomial.

`-2/3 m^3 - 5 m^2 + 7m -1`

Practice Set 3.1 | Q 3.1 | Page 39

Write the polynomial in x using the given information.

Monomial with degree 7

Practice Set 3.1 | Q 3.2 | Page 39

Write the polynomial in x using the given information.

Binomial with degree 35

Practice Set 3.1 | Q 3.3 | Page 39

Write the polynomial in x using the given information.

Trinomial with degree 8

Practice Set 3.1 | Q 4.1 | Page 40

Write the degree of the given polynomial.

`sqrt 5`

Practice Set 3.1 | Q 4.2 | Page 40

Write the degree of the given polynomial.

`x^0`

Practice Set 3.1 | Q 4.3 | Page 40

Write the degree of the given polynomial.

`x^2`

Practice Set 3.1 | Q 4.4 | Page 40

Write the degree of the given polynomial.

`sqrt2m^10 - 7`

Practice Set 3.1 | Q 4.5 | Page 40

Write the degree of the given polynomial.

`2p - sqrt 7`

Practice Set 3.1 | Q 4.6 | Page 40

Write the degree of the given polynomial.

`7y - y^3 + y^5`

Practice Set 3.1 | Q 4.7 | Page 40

Write the degree of the given polynomial.

xyz + xy - z

Practice Set 3.1 | Q 4.8 | Page 40

Write the degree of the given polynomial.

`m^3n^7 -3m^5n + mn`

Practice Set 3.1 | Q 5.1 | Page 40

Classify the following polynomial as linear, quadratic and cubic polynomial.

2x2 + 3 x + 1

Practice Set 3.1 | Q 5.2 | Page 40

Classify the following polynomial as linear, quadratic and cubic polynomial.

5p

Practice Set 3.1 | Q 5.3 | Page 40

Classify the following polynomial as linear, quadratic and cubic polynomial.

`sqrt 2  y - 1/2`

Practice Set 3.1 | Q 5.4 | Page 40

Classify the following polynomial as linear, quadratic and cubic polynomial.

`m^3 + 7m^2 + 5/2m - sqrt 7`

Practice Set 3.1 | Q 5.5 | Page 40

Classify the Following Polynomial as Linear, Quadratic and Cubic Polynomial.

`a^2`

Practice Set 3.1 | Q 5.6 | Page 40

Classify the following polynomial as linear, quadratic and cubic polynomial.

`3r^3`

Practice Set 3.1 | Q 6.1 | Page 40

Write the following polynomial in standard form.

`m^3 + 3 + 5m`

Practice Set 3.1 | Q 6.2 | Page 40

Write the following polynomial in standard form.

`-7y + y^5 + 3y^3 - 1/2 +2y^4 -y^2`

Practice Set 3.1 | Q 7.1 | Page 40

Write the following polynomial in coefficient form.

`x^3 - 2`

Practice Set 3.1 | Q 7.2 | Page 40

Write the following polynomial in coefficient form.

5y

Practice Set 3.1 | Q 7.3 | Page 40

Write the following polynomial in coefficient form.

`2m^4 -3m^2 + 7`

Practice Set 3.1 | Q 7.4 | Page 40

Write the following polynomial in coefficient form.

`-2/3`

Practice Set 3.1 | Q 8.1 | Page 40

Write the polynomial in index form.

(1, 2, 3)

Practicr Set 3.1 | Q 8.2 | Page 40

Write the polynomial in index form.

(5, 0, 0, 0, -1) 

Practice Set 3.1 | Q 8.3 | Page 40

Write the polynomial in index form.

(-2 ,2,-2 , 2)

Practice Set 3.1 | Q 9 | Page 40

Write the appropriate polynomials in the boxes.

Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra Chapter 3 Polynomials Exercise Practice Set 3.2 [Page 43]

Practice Set 3.2 | Q 1.1 | Page 43

Use the given letter to write the answer.

There are ‘a’ trees in the village Lat. If the number of trees increases every year by ‘b’, then how many trees will there be after ‘x’ years?

Practice Set 3.2 | Q 1.2 | Page 43

Use the Given Letter to Write the Answer.

For the parade there are y students in each row and x such row are formed. Then, how many students are there for the parade in all ? 
Practice Set 3.2 | Q 1.3 | Page 43

Use the given letter to write the answer.

The tens and units place of a two digit number is m and n respectively. Write the polynomial which represents the two digit number.

Practice Set 3.2 | Q 2.1 | Page 43

Add the Given Polynomial.

`x^3 - 2x^2 - 9 ;  5x^3 + 2x + 9`

Practice Set 3.2 | Q 2.2 | Page 43

Add the given polynomial.

`-7m^4 +5m^3 + sqrt2 ;   5m^4 - 3m^3 + 2m&2 + 3m - 6`

Practice Set 3.2 | Q 2.3 | Page 43

Add the given polynomial.

`2y^2 + 7y + 5  ;  3y + 9  ;  3y^2 - 4y - 3`

Practice Set 3.2 | Q 3.1 | Page 43

Subtract the second polynomial from the first.

`x^2 - 9x + sqrt 3  ;  -19x + sqrt 3 +7x^2`

Practice Set 3.2 | Q 3.2 | Page 43

Subtract the second polynomial from the first.

`2ab^2 + 3a^2b - 4ab ; 3ab - 8ab^2 + 2a^2b`

Practice Set 3.2 | Q 4.1 | Page 43

Multiply the given polynomial.

`2x  ;  x^2 - 2x - 1`

Practice Set 3.2 | Q 4.2 | Page 43

Multiply the given polynomial.

`x^5 - 1  ;  x^3 +2x^2 + 2`

Practice Set 3.2 | Q 4.3 | Page 43

Multiply the given polynomial.

`2y + 1 ; y^2 - 2y^3 + 3y`

Practice Set 3.2 | Q 5.1 | Page 43

Divide first polynomial by second polynomial and write the answer in the form ‘Dividend = Divisor × Quotient + Remainder’.

`x^3 - 64 ; x - 4`

Practice Set 3.2 | Q 5.2 | Page 43

Divide first polynomial by second polynomial and write the answer in the form ‘Dividend = Divisor × Quotient + Remainder’.

`5x^5 + 4x^4 - 3x^3 + 2x^2 +2`

Practice Set 3.2 | Q 6 | Page 43

Write down the information in the form of algebraic expression and simplify.

There is a rectangular farm with length `(2a^2 + 3b^2)` metre and breadth `(a^2 + b^2)` metre. The farmer used a square shaped plot of the farm to build a house. The side of the plot was `(a^2 -  b^2)` metre.
What is the area of the remaining part of the farm ?

Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra Chapter 3 Polynomials Exercise Practice Set 3.3 [Page 46]

Practice Set 3.3 | Q 1.1 | Page 46
Divide each of the following polynomial by synthetic division method and also by
linear division method. Write the quotient and the remainder.
`(2m^2 - 3m + 10) ÷ (m - 5)`
Practice Set 3.3 | Q 1.2 | Page 46

Divide each of the following polynomial by synthetic division method and also by linear division method. Write the quotient and the remainder.

`(x^4 + 2x^3 +3x^2 + 4x + 5) ÷ (x + 2)`

Practice Set 3.3 | Q 1.3 | Page 46

Divide each of the following polynomial by synthetic division method and also by linear division method. Write the quotient and the remainder.

`(y^3 - 216) ÷ (y - 6)`

Practice Set 3.3 | Q 1.4 | Page 46

Divide each of the following polynomial by synthetic division method and also by linear division method. Write the quotient and the remainder.

`(2x^4 + 3x^3 + 4x - 2x^2) ÷ (x + 3)`

Practice Set 3.3 | Q 1.5 | Page 46

Divide each of the following polynomial by synthetic division method and also by linear division method. Write the quotient and the remainder.

`(x^4 - 3x^2 - 8) ÷ (x + 4)`

Practice Set 3.3 | Q 1.6 | Page 46
Divide each of the following polynomial by synthetic division method and also by linear division method. Write the quotient and the remainder.
`(y^3 - 3y^2 + 5y - 1) ÷ (y - 1)`

Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra Chapter 3 Polynomials Exercise Practice Set 3.4 [Page 48]

Practice Set 3.4 | Q 1 | Page 48

For x = 0 find the value of the polynomial `x^2 - 5x + 5.`

Practice Set 3.4 | Q 2 | Page 48

If p(y) = `y^2 - 3sqrt2 + 1` then find  `p (3sqrt 2)`.

Practice Set 3.4 | Q 3 | Page 48

If `p(m) = m^3 + 2m^2 - m + 10` then p(a) + p(-a) = ?

Practice Set 3.4 | Q 4 | Page 48

If `p(y) = 2y^3 - 6y^2 - 5y + 7` then finf p(2).

Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra Chapter 3 Polynomials Exercise Practice Set 3.5 [Page 53]

Practice Set 3.5 | Q 1.1 | Page 53

Find the value of the polynomial `2x - 2x^3 + 7` using given values for x.

x = 3

Practice Set 3.5 | Q 1.2 | Page 53

Find the value of the polynomial `2x - 2x^3 + 7` using givem values for x.

x = -1

Practice Set 3.5 | Q 1.3 | Page 53

Find the value of the polynomial `2x - 2x^3 + 7` using given values for x.

x = 0

Practice Set 3.5 | Q 2.1 | Page 53

For each of the following polynomial, find p(1) , p(0) and p(-2).

`p(x) = x^3`

Practice Set 3.5 | Q 2.2 | Page 53

For each of the following polynomial, find  p(1) , p(0) and p(-2).

`p(y) = y^2 - 2y + 5`

Practice Set 3.5 | Q 2.3 | Page 53

For each of the following polynomial, find p(1) , p(0) and p(-2).

`p(x) = x^4 - 2x^2 - x` 

Practice Set 3.5 | Q 3 | Page 53

If the value of the polynomial `m^3 + 2m + a` is 12 for m = 2,  then  find the value of a.

Practice Set 3.5 | Q 4 | Page 53

For the polynomial `mx^`- x + 3 if p(-1) = 7 then find m .

Practice Set 3.5 | Q 5.1 | Page 53

Divide the first polynomial by the second polynomial and find the remainder using factor theorem .

`(x^2 - 7x + 9) ; (x  1)`

Practice Set 3.5 | Q 5.2 | Page 53

Divide the first polynomial by the second polynomial and find the remainder using factor theorem .

`(2x^3 - 2x^2 + ax - a) ; (x - a)`

Practice Set 3.5 | Q 5.3 | Page 53

Divide the first polynomial by the second polynomial and find the remainder using factor theorem .

`(54m^3 + 18 m^2 - 27m + 5) ; (m - 3)`

Practice Set 3.5 | Q 6 | Page 53

If the polynomial `y^3 - 5y^2 + 7y + m` is divided by y + 2 and the remainder is 50 then find the value of m.

Practice Set 3.5 | Q 7 | Page 53

Use factor theorem to determine whether x + 3 is factor of x 2 + 2x − 3 or not. 

Practice Set 3.5 | Q 8 | Page 53

If (x - 2) is a factor of `x^3 - mx^2 + 10x - 20` then find the value of m.

Practice Set 3.5 | Q 9.1 | Page 53

By using factor theorem in the following example, determine whether q ( x ) is a factor p ( x ) or not.

`p(x) = x^3 - x^2 - x - 1 , q(x) = x - 1`

Practice Set 3.5 | Q 9.2 | Page 53

By using factor theorem in the following example, determine whether q ( x ) is a factor p ( x ) or not.

`p(x) = 2x^3 - x^2 - 45 ,  q(x) = x - 3`

Practice Set 3.5 | Q 10 | Page 53

If ( x31 + 31) is divided by (x + 1) then find the remainder. 

Practice Set 3.5 | Q 11 | Page 53

Show that m - 1 is a factor of m21 - 1 and m22 - 1.

Practice Set 3.5 | Q 12 | Page 53

If x - 2 and  `x - 1/2` both are the factors of the polynomial  nx2 − 5x + m, then show that  m = n = 2

Practice Set 3.5 | Q 13.1 | Page 53

If p (x) = 2+5x then p(2) + p(-2) - p(1).

Practice Set 3.5 | Q 13.2 | Page 53

`p(x) = 2x^2 - 5sqrt 3 x + 5` then  `p(5 sqrt 3)`

Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra Chapter 3 Polynomials Exercise Practice Set 3.6 [Pages 54 - 55]

Practice Set 3.6 | Q 1.1 | Page 54

Find the Factors of the Polynomial Given Below.

2x2 + x – 1

Practice Set 3.6 | Q 1.2 | Page 54

Find the factors of the polynomial given below.

2m2 + 5m – 3

Practice Set 3.6 | Q 1.3 | Page 54

Find the factors of the polynomial given below.

12x2 + 61x + 77

Practice Set 3.6 | Q 1.4 | Page 54

Find the factors of the polynomial given below.

3y2 – 2y – 1

Practice Set 3.6 | Q 1.5 | Page 54

Find the factors of the polynomial given below.

`sqrt 3 x^2 + 4x + sqrt 3`

Practice Set 3.6 | Q 1.6 | Page 54

Find the factors of the polynomial given below.

`1/2x^2 - 3x + 4`

Practice Set 3.6 | Q 2.1 | Page 55

Factorize the following polynomial.

(x2 – x)2 – 8 (x2 – x) + 12

Practice Set 3.6 | Q 2.2 | Page 55

Factorize the following polynomial.

(x – 5)2 – (5x – 25) – 24

Practice Set 3.6 | Q 2.3 | Page 55

Factorize the following polynomial.

 (x2 – 6x)2 – 8 (x2 – 6x + 8) – 64

Practice Set 3.6 | Q 2.4 | Page 55

Factorize the following polynomial.

(x2 – 2x + 3) (x2 – 2x + 5) – 35 

Practice Set 3.6 | Q 2.5 | Page 55

Factorize the following polynomial.

(y + 2) (y – 3) (y + 8) (y + 3) + 56 

Practice Set 3.6 | Q 2.6 | Page 55

Factorize the following polynomial.

 (y2 + 5y) (y2 + 5y – 2) – 24

Practice Set 3.6 | Q 2.7 | Page 55

Factorize the following polynomial.

(x – 3) (x – 4)2 (x – 5) – 6 

Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra Chapter 3 Polynomials Exercise Problem Set 3 [Pages 55 - 56]

Problem Set 3 | Q 1.01 | Page 55

Write the correct alternative answer for the following question.

Which of the following is a polynomial ?

  • `x/y`

  • `x^(sqrt2) - 3x`

  • `x^(-2) + 7`

  • `sqrt2 x^2 + 1/2`

Problem Set 3 | Q 1.02 | Page 55

Write the correct alternative answer for  the following question.

What is the degree of the polynomial `sqrt 7` ?

  • `1/2`

  • 5

  • 2

  • 0

Problem Set 3 | Q 1.03 | Page 55

Write the correct alternative answer for  the following question.

What is the degree of the 0 polynomial ?

  • 0

  • 1

  • undefined

  • any real number

Problem Set 3 | Q 1.04 | Page 55

Write the correct alternative answer for the following question.

What is the degree of the polynomial 2x+ 5x+ 7 ? 

  • 3

  • 2

  • 5

  • 7

Problem Set 3 | Q 1.05 | Page 55

Write the correct alternative answer for the following question.

What is the coefficient form of `x^3 - 1 ` ?

  • (1 , -1)

  • (3 , -1)

  • (1 , 0 , 0, -1)

  • (1 , 3 , -1)

Problem Set 3 | Q 1.06 | Page 55

Write the correct alternative answer for the following question.

`p(x) = x^2 - 7 sqrt 7 x + 3  "then " p(7 sqrt 7) = ?`

  • 3

  • `7sqrt7`

  • `42 sqrt 7 + 3`

  • `49 sqrt 7`

Problem Set 3 | Q 1.07 | Page 55

Write the correct alternative answer for  the following question.

When x = -1 , what is the value of the polynomial 2x+ 2x ? 

  • 4

  • 2

  • -2

  • -4

Problem Set 3 | Q 1.08 | Page 55

Write the correct alternative answer for the following question.

If x - 1 , what is a factor of the polynomial `3x^2 + mx `  then find the value of m. 

  • 2

  • -2

  • -3

  • 3

Problem Set 3 | Q 1.09 | Page 55

Write the correct alternative answer for the following question.

Multiply  ( x2 - 3) (2x - 7x + 4) and write the degree of the product. 

  • 5

  • 3

  • 2

  • 0

Problem Set 3 | Q 1.1 | Page 55

Write the correct alternative answer for  the following question.

Which of the following is a linear polynomial ?

  • x + 5

  • `x^2 + 5`

  • `x^3 + 5`

  • `x^4 + 5`

Problem Set 3 | Q 2.1 | Page 56

Write the degree of the polynomial for the following.

5 + 3x4 

Problem Set 3 | Q 2.2 | Page 56

Write the degree of the polynomial for the following.

7

Problem Set 3 | Q 2.3 | Page 56

Write the degree of the polynomial for the following.

ax+ bx( a, b are constants.)

Problem Set 3 | Q 3.1 | Page 56

Write the following polynomial in standard form.

4x2 + 7x4- x3 - x  + 9

Problem Set 3 | Q 3.2 | Page 56

Write the following polynomial in standard form. 

p + 2 p3 + 10 p2 + 5 p4 - 8

Problem Set 3 | Q 4.1 | Page 56
Write the following polynomial in coefficient form.
x4 + 16  
Problem Set 3 | Q 4.2 | Page 56
Write the following polynomial in coefficient form.
m+ 2m2 + 3m + 15
Problem Set 3 | Q 5.1 | Page 56

Write the index form of the polynomial using variable x from its coefficient form.

(3, -2, 0, 7, 18)

Problem Set 3 | Q 5.2 | Page 56

Write the index form of the polynomial using variable x from its coefficient form. 

(6, 1, 0, 7)

Problem Set 3 | Q 5.3 | Page 56

Write the index form of the polynomial using variable x from its coefficient form.

(4, 5, -3, 0)

Problem Set 3 | Q 6.1 | Page 56

Add the following polynomial.

7x4 - 2x3 + x + 10 ; 3x4 + 15x3 + 9x2 - 8x + 2

Problem Set 3 | Q 6.2 | Page 56

Add the following polynomial.

3p3q+ 2p2q + 7 ; 2p2q + 4pq - 2p3q

Problem Set 3 | Q 7.1 | Page 56

Subtract the second polynomial from the first.

5x2 - 2y + 9 ; 3x2 + 5y - 7

Problem Set 3 | Q 7.2 | Page 56

Subtract the second polynomial from the first.

2x+ 3x + 5 ; x 2 -2x + 3

Problem Set 3 | Q 8.1 | Page 56

Multiply the following polynomial.

(m3 - 2m + 3)(m4 - 2m+ 3m + 2)

Problem Set 3 | Q 8.2 | Page 56

Multiply the following polynomial.

(5m3 - 2)(m2 - m + 3)

Problem Set 3 | Q 9 | Page 56

Divide polynomial 3x3 - 8x2 + x + 7 by x - 3 using synthetic method and write the quotient and remainder.

Problem Set 3 | Q 10 | Page 56

For which the value of m, x + 3 is the factor of the polynomial x3 - 2mx + 21 ?

Problem Set 3 | Q 11 | Page 56

At the end of the year 2016, the population of villages Kovad, Varud, Chikhali is 5x- 3 y2 , 7 y+ 2 xy and 9 x+ 4 xy respectively. At the beginning of the year 2017, x+ xy - y2 , 5 xy and 3 x2 + xy persons from each of the three villages respectively went to another village for education then what is the remaining total population of these three villages ?

Problem Set 3 | Q 12 | Page 56

Polynomials bx+ x + 5 and bx3 -2x + 5 are divided by polynomial x - 3 and the remainders are m and n respectively. If m - n = 0 then find the value of b.

Problem Set 3 | Q 13 | Page 56

Simplify

(8m2 + 3m - 6) - (9m - 7)+ (3m2 - 2m +4)

Problem Set 3 | Q 14 | Page 56

Which polynomial is to be subtracted from x2 +  13x + 7 to get the polynomial  3x+ 5x - 4?

Problem Set 3 | Q 15 | Page 56

Which polynomial is to be added to 4m + 2n + 3 to get the polynomial 6m + 3n + 10?

Chapter 3: Polynomials

Practice Set 3.1Practicr Set 3.1Practice Set 3.2Practice Set 3.3Practice Set 3.4Practice Set 3.5Practice Set 3.6Problem Set 3
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Maharashtra state board Class 9 Mathematics 1 Algebra - Shaalaa.com

Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra chapter 3 - Polynomials

Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra chapter 3 (Polynomials) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Maharashtra state board Class 9 Mathematics 1 Algebra solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Maharashtra state board Class 9 Mathematics 1 Algebra chapter 3 Polynomials are Introduction of Polynomials, Degree of a Polynomial, Operations on Polynomials, Synthetic Division, Value of a Polynomial, Remainder Theorem, Factor Theorem.

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