#### Chapters

## Chapter 3: Polynomials

#### 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]

State whether the given algebraic expression are polynomial? Justify.

`y + 1/y`

State whether the given algebraic expression are polynomial? Justify.

`2 - 5 sqrt x`

State whether the given algebraic expression are polynomial? Justify.

`x^2 + 7x + 9`

State Whether the Given Algebraic Expression Are Polynomial? Justify.

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

State whether the given algebraic expression are polynomial? Justify.

10

Write the coefficient of m^{3} in the given polynomial.

`m^3`

Write the coefficient of m^{3} in the given polynomial.

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

Write the coefficient of m^{3} in the given polynomial.

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

Write the polynomial in x using the given information.

Monomial with degree 7

Write the polynomial in x using the given information.

Binomial with degree 35

Write the polynomial in x using the given information.

Trinomial with degree 8

Write the degree of the given polynomial.

`sqrt 5`

Write the degree of the given polynomial.

`x^0`

Write the degree of the given polynomial.

`x^2`

Write the degree of the given polynomial.

`sqrt2m^10 - 7`

Write the degree of the given polynomial.

`2p - sqrt 7`

Write the degree of the given polynomial.

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

Write the degree of the given polynomial.

xyz + xy - z

Write the degree of the given polynomial.

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

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

2x^{2} + 3 x + 1

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

5p

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

`sqrt 2 y - 1/2`

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

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

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

`a^2`

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

`3r^3`

Write the following polynomial in standard form.

`m^3 + 3 + 5m`

Write the following polynomial in standard form.

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

Write the following polynomial in coefficient form.

`x^3 - 2`

Write the following polynomial in coefficient form.

5y

Write the following polynomial in coefficient form.

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

Write the following polynomial in coefficient form.

`-2/3`

Write the polynomial in index form.

(1, 2, 3)

Write the polynomial in index form.

(5, 0, 0, 0, -1)

Write the polynomial in index form.

(-2 ,2,-2 , 2)

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]

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?

Use the Given Letter to Write the Answer.

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.

Add the Given Polynomial.

`x^3 - 2x^2 - 9 ; 5x^3 + 2x + 9`

Add the given polynomial.

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

Add the given polynomial.

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

Subtract the second polynomial from the first.

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

Subtract the second polynomial from the first.

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

Multiply the given polynomial.

`2x ; x^2 - 2x - 1`

Multiply the given polynomial.

`x^5 - 1 ; x^3 +2x^2 + 2`

Multiply the given polynomial.

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

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

`x^3 - 64 ; x - 4`

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`

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]

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)`

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)`

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)`

`(x^4 - 3x^2 - 8) ÷ (x + 4)`

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

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

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

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

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]

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

x = 3

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

x = -1

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

x = 0

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

`p(x) = x^3`

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

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

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

`p(x) = x^4 - 2x^2 - x`

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

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

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

`(x^2 - 7x + 9) ; (x 1)`

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

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

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

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

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.

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

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

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`

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`

If ( x^{31} + 31) is divided by (x + 1) then find the remainder.

Show that m - 1 is a factor of m^{21} - 1 and m^{22} - 1.

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

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

`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]

Find the Factors of the Polynomial Given Below.

2x^{2} + x – 1

Find the factors of the polynomial given below.

2m^{2} + 5m – 3

Find the factors of the polynomial given below.

12x^{2} + 61x + 77

Find the factors of the polynomial given below.

3y^{2} – 2y – 1

Find the factors of the polynomial given below.

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

Find the factors of the polynomial given below.

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

Factorize the following polynomial.

(x^{2} – x)^{2} – 8 (x^{2} – x) + 12

Factorize the following polynomial.

(x – 5)^{2} – (5x – 25) – 24

Factorize the following polynomial.

(x^{2} – 6x)^{2} – 8 (x^{2} – 6x + 8) – 64

Factorize the following polynomial.

(x^{2} – 2x + 3) (x^{2} – 2x + 5) – 35

Factorize the following polynomial.

(y + 2) (y – 3) (y + 8) (y + 3) + 56

Factorize the following polynomial.

(y^{2} + 5y) (y^{2} + 5y – 2) – 24

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]

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`

Write the correct alternative answer for the following question.

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

`1/2`

5

2

0

Write the correct alternative answer for the following question.

What is the degree of the 0 polynomial ?

0

1

undefined

any real number

Write the correct alternative answer for the following question.

What is the degree of the polynomial 2x^{2 }+ 5x^{3 }+ 7 ?

3

2

5

7

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)

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`

Write the correct alternative answer for the following question.

When x = -1 , what is the value of the polynomial 2x^{3 }+ 2x ?

4

2

-2

-4

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

Write the correct alternative answer for the following question.

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

5

3

2

0

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`

Write the degree of the polynomial for the following.

5 + 3x^{4}

Write the degree of the polynomial for the following.

7

Write the degree of the polynomial for the following.

ax^{7 }+ bx^{9 }( a, b are constants.)

Write the following polynomial in standard form.

4x^{2} + 7x^{4}- x^{3} - x + 9

Write the following polynomial in standard form.

p + 2 p^{3} + 10 p^{2} + 5 p^{4} - 8

^{4}+ 16

^{5 }+ 2m

^{2}+ 3m + 15

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

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

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

(6, 1, 0, 7)

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

(4, 5, -3, 0)

Add the following polynomial.

7x^{4} - 2x^{3 }+ x + 10 ; 3x^{4} + 15x^{3} + 9x^{2} - 8x + 2

Add the following polynomial.

3p^{3}q+ 2p^{2}q + 7 ; 2p^{2}q + 4pq - 2p^{3}q

Subtract the second polynomial from the first.

5x^{2} - 2y + 9 ; 3x^{2} + 5y - 7

Subtract the second polynomial from the first.

2x^{2 }+ 3x + 5 ; x ^{2} -2x + 3

Multiply the following polynomial.

(m^{3} - 2m + 3)(m^{4} - 2m^{2 }+ 3m + 2)

Multiply the following polynomial.

(5m^{3} - 2)(m^{2} - m + 3)

Divide polynomial 3x^{3} - 8x^{2} + x + 7 by x - 3 using synthetic method and write the quotient and remainder.

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

At the end of the year 2016, the population of villages Kovad, Varud, Chikhali is 5x^{2 }- 3 y^{2} , 7 y^{2 }+ 2 xy and 9 x^{2 }+ 4 xy respectively. At the beginning of the year 2017, x^{2 }+ xy - y^{2} , 5 xy and 3 x^{2} + 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 ?

Polynomials bx^{2 }+ x + 5 and bx^{3} -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.

Simplify

(8m^{2} + 3m - 6) - (9m - 7)+ (3m^{2} - 2m +4)

Which polynomial is to be subtracted from x^{2} + 13x + 7 to get the polynomial 3x^{2 }+ 5x - 4?

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

## Chapter 3: Polynomials

## 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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