#### Chapters

## Chapter 3: Algebra

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 3 Algebra Exercise 3.1 [Pages 87 - 88]

Identify the following expression is polynomial. If not give reason:

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

Identify the following expression is polynomial. If not give reason:

x^{2}(x – 1)

Identify the following expression is polynomial. If not give reason:

`1/x(x + 5)`

Identify the following expression is polynomial. If not give reason:

`1/(x^(-2)) + 1/(x^(-1)) + 7`

Identify the following expression is polynomial. If not give reason:

`sqrt(5)x^2 + sqrt(3)x + sqrt(2)`

Identify the following expression is polynomial. If not give reason:

`"m"^2 - root(3)("m") + 7"m" - 10`

Write the coefficient of x^{2} and x in the following polynomials

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

Write the coefficient of x^{2} and x in the following polynomials

`6 - 2x^2 + 3x^3 - sqrt(7)x`

Write the coefficient of x^{2} and x in the following polynomials

πx^{2} – x + 2

Write the coefficient of x^{2} and x in the following polynomials

`sqrt(3)x^2 + sqrt(2)x + 0.5`

Write the coefficient of x^{2} and x in the following polynomials

`x^2 - 7/2 x + 8`

Find the degree of the following polynomial

`2sqrt(5)"p"^4 - (8"p"^3)/sqrt(3) + (2"p"^2)/7`

Find the degree of the following polynomial

`1 - sqrt(2)y^2 + y^7`

Find the degree of the following polynomial

`(x^3 - x^4 + 6x^6)/x^2`

Find the degree of the following polynomial

x^{3}(x^{2} + x)

Find the degree of the following polynomial

3x^{4} + 9x^{2} + 27x^{6 }

Rewrite the following polynomial in standard form

`x - 9 + sqrt(7)x^3 + 6x^2`

Rewrite the following polynomial in standard form

`sqrt(2)x^2 - 7/2 x^4 + x - 5x^3`

Rewrite the following polynomial in standard form

`7x^3 - 6/5x^2 + 4x - 1`

Rewrite the following polynomial in standard form

`y^2 + sqrt(5)y^3 - 11 - 7/3y + 9y^4`

Add the following polynomials and find the degree of the resultant polynomial

p(x) = 6x^{2} – 7x + 2, q(x) = 6x^{3} – 7x + 15

Add the following polynomials and find the degree of the resultant polynomial

h(x) = 7x^{3} – 6x + 1, f(x) = 7x^{2} + 17x – 9

Add the following polynomials and find the degree of the resultant polynomial

f(x) = 16x^{4} – 5x^{2} + 9, g(x) = −6x^{3} + 7x – 15

Subtract the second polynomial from the first polynomial and find the degree of the resultant polynomial

p(x) = 7x^{2} + 6x – 1, q(x) = 6x – 9

Subtract the second polynomial from the first polynomial and find the degree of the resultant polynomial

f(y) = 6y^{2} – 7y + 2, g(y) = 7y + y^{3}

Subtract the second polynomial from the first polynomial and find the degree of the resultant polynomial

h(z) = z^{5} – 6z^{4} + z, f(z) = 6z^{2} + 10z – 7

What should be added to 2x^{3} + 6x^{2} – 5x + 8 to get 3x^{3} – 2x^{2} + 6x + 15?

What must be subtracted from 2x^{4} + 4x^{2} – 3x + 7 to get 3x^{3} – x^{2} + 2x + 1?

Multiply the following polynomials and find the degree of the resultant polynomial:

p(x) = x^{2} – 9, q(x) = 6x^{2} + 7x – 2

Multiply the following polynomials and find the degree of the resultant polynomial:

f(x) = 7x + 2, g(x) = 15x – 9

Multiply the following polynomials and find the degree of the resultant polynomial:

h(x) = 6x^{2} – 7x + 1, f(x) = 5x – 7

The cost of a chocolate is Rs. (x + y) and Amir bought (x + y) chocolates. Find the total amount paid by him in terms of x and y. If x = 10, y = 5 find the amount paid by him

The length of a rectangle is (3x + 2) units and it’s breadth is (3x – 2) units. Find its area in terms of x. What will be the area if x = 20 units

p(x) is a polynomial of degree 1 and q(x) is a polynomial of degree 2. What kind of the polynomial is p(x) × q(x)?

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 3 Algebra Exercise 3.2 [Pages 91 - 92]

Find the value of the polynomial f(y) = 6y – 3y^{2} + 3 at y = 1

Find the value of the polynomial f(y) = 6y – 3y^{2} + 3 at y = –1

Find the value of the polynomial f(y) = 6y – 3y^{2} + 3 at y = 0

If p(x) = `x^2 - 2sqrt(2)x + 1`, find `"p"(2sqrt(2))`

Find the zero of the polynomial of the following:

p(x) = x – 3

Find the zero of the polynomial of the following:

p(x) = 2x + 5

Find the zero of the polynomial of the following:

q(y) = 2y – 3

Find the zero of the polynomial of the following :

f(z) = 8z

Find the zero of the polynomial in the following:

h(x) = ax + b, a ≠ 0, a, b ∈ R

Find the zero of the polynomial of the following:

p(x) = ax when a ≠ 0

Find the roots of the polynomial equation

5x – 6 = 0

Find the roots of the polynomial equation

x + 3 = 0

Find the roots of the polynomial equation

10x + 9 = 0

Find the roots of the polynomial equation

9x – 4 = 0

Verify whether the following are zeros of the polynomial indicated against them, or not

p(x) = 2x − 1, x = `1/2`

Verify whether the following are zeros of the polynomial, indicated against them, or not

p(x) = x^{3} – 1, x = 1

Verify whether the following are zeros of the polynomial, indicated against them, or not

p(x) = ax + b, x = `(-"b")/"a"`

Verify whether the following are zeros of the polynomial, indicated against them, or not

p(x) = (x + 3) (x – 4), x = −3, x = 4

Find the number of zeros of the following polynomial represented by their graph

Find the number of zeros of the following polynomial represented by their graph

Find the number of zeros of the following polynomial represented by their graph

Find the number of zeros of the following polynomial represented by their graph

Find the number of zeros of the following polynomial represented by their graph

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 3 Algebra Exercise 3.3 [Pages 96 - 97]

Check whether p(x) is a multiple of g(x) or not

p(x) = x^{3} – 5x^{2} + 4x – 3, g(x) = x – 2

By remainder theorem, find the remainder when, p(x) is divided by g(x) where, p(x) = x^{3} – 2x^{2} – 4x – 1; g(x) = x + 1

By remainder theorem, find the remainder when, p(x) is divided by g(x) where, p(x) = 4x^{3} – 12x^{2} + 14x – 3; g(x) = 2x – 1

By remainder theorem, find the remainder when, p(x) is divided by g(x) where, p(x) = x^{3} – 3x^{2} + 4x + 50; g(x) = x – 3

Find the remainder when 3x^{3} – 4x^{2} + 7x – 5 is divided by (x + 3)

What is the remainder when x^{2018} + 2018 is divided by x – 1

For what value of k is the polynomial p(x) = 2x^{3} – kx^{2} + 3x + 10 exactly divisible by (x – 2)

If two polynomials 2x^{3} + ax^{2} + 4x – 12 and x^{3} + x^{2} – 2x + a leave the same remainder when divided by (x – 3), find the value of a and also find the remainder.

Determine whether (x – 1) is a factor of the following polynomials:

x^{3} + 5x^{2} – 10x + 4

Determine whether (x – 1) is a factor of the following polynomials:

x^{4} + 5x^{2} – 5x + 1

Using factor theorem, show that (x – 5) is a factor of the polynomial

2x^{3} – 5x^{2} – 28x + 15

Determine the value of m, if (x + 3) is a factor of x^{3} – 3x^{2} – mx + 24

If both (x − 2) and `(x - 1/2)` is the factors of ax^{2} + 5x + b, then show that a = b

If (x – 1) divides the polynomial kx^{3} – 2x^{2} + 25x – 26 without remainder, then find the value of k

Check if (x + 2) and (x – 4) are the sides of a rectangle whose area is x^{2} – 2x – 8 by using factor theorem

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 3 Algebra Exercise 3.4 [Pages 101 - 102]

Expand the following:

(2x + 3y + 4z)^{2 }

Expand the following:

(−p + 2q + 3r)^{2}

Expand the following:

(2p + 3)(2p – 4)(2p – 5)

Expand the following:

(3a + 1)(3a – 2)(3a + 4)

Using algebraic identity, find the coefficients of x^{2}, x and constant term without actual expansion

(x + 5)(x + 6)(x + 7)

Using algebraic identity, find the coefficients of x^{2}, x and constant term without actual expansion

(2x + 3)(2x – 5)(2x – 6)

If (x + a)(x + b)(x + c) = x^{3} + 14x^{2} + 59x + 70, find the value of a + b + c

If (x + a)(x + b)(x + c) = x^{3} + 14x^{2} + 59x + 70, find the value of `1/"a" + 1/"b" + 1/"c"`

If (x + a)(x + b)(x + c) = x^{3} + 14x^{2} + 59x + 70, find the value of a^{2} + b^{2} + c^{2 }

If (x + a)(x + b)(x + c) = x^{3} + 14x^{2} + 59x + 70, find the value of `"a"/"bc" + "b"/"ac" + "c"/"ab"`

Expand: (3a – 4b)^{3 }

Expand: `[x + 1/y]^3`

Evaluate the following by using identities:

98^{3}

Evaluate the following by using identities:

1001^{3}

If (x + y + z) = 9 and (xy + yz + zx) = 26, then find the value of x^{2} + y^{2} + z^{2}

Find 27a^{3} + 64b^{3}, if 3a + 4b = 10 and ab = 2

Find x^{3} – y^{3}, if x – y = 5 and xy = 14.

If `"a" + 1/"a"` = 6, then find the value of `"a"^3 + 1/"a"^3`

If `x^2 + 1/x^2` = 23, then find the value of `x + 1/x` and `x^3 + 1/x^3`

If `(y - 1/y)^3` = 27, then find the value of `y^3 - 1/y^3`

Simplify: (2a + 3b + 4c) (4a^{2} + 9b^{2} + 16c^{2} – 6ab – 12bc – 8ca)

Simplify: (x – 2y + 3z) (x^{2} + 4y^{2} + 9z^{2} + 2xy + 6yz – 3xz)

By using identity evaluate the following:

7^{3} – 10^{3} + 3^{3 }

By using identity evaluate the following:

`1 + 1/8 - 27/8`

If 2x – 3y – 4z = 0, then find 8x^{3} – 27y^{3} – 64z^{3 }

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 3 Algebra Exercise 3.5 [Page 105]

Factorise the following expression:

2a² + 4a²b + 8a²c

Factorise the following expression:

ab – ac – mb + mc

Factorise the following:

x² + 4x + 4

Factorise the following:

3a² – 24ab + 48b²

Factorise the following:

x^{5} – 16x

Factorise the following:

`"m"^2 + 1/"m"^2 - 23`

Factorise the following:

6 – 216x^{2 }

Factorise the following:

`"a"^2 + 1/"a"^2 - 18`

Factorise the following:

4x^{2} + 9y^{2} + 25z^{2} + 12xy + 30yz + 20xz

Factorise the following:

25x^{2} + 4y^{2} + 9z^{2} – 20xy + 12yz – 30xz

Factorise the following:

8x^{3} + 125y^{3}

Factorise the following:

27x^{3} – 8y^{3}

Factorise the following:

a^{6} – 64

Factorise the following:

x^{3} + 8y^{3} + 6xy – 1

Factorise the following:

l^{3} – 8m^{3} – 27n^{3} – 18lmn

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 3 Algebra Exercise 3.6 [Page 107]

Factorise the following:

x² + 10x + 24

Factorise the following:

z² + 4z – 12

Factorise the following:

p² – 6p – 16

Factorise the following:

t² + 72 – 17t

Factorise the following:

y^{2} – 16y – 80

Factorise the following:

a^{2} + 10a – 600

Factorise the following:

2a^{2} + 9a + 10

Factorise the following:

5x^{2} – 29xy – 42y^{2}

Factorise the following:

9 – 18x + 8x^{2}

Factorise the following:

6x^{2} + 16xy + 8y^{2}

Factorise the following:

12x^{2} + 36x^{2}y + 27y^{2}x^{2}

Factorise the following:

(a + b)^{2} + 9(a + b) + 18

Factorise the following:

(p – q)^{2} – 6(p – q) – 16

Factorise the following:

m^{2} + 2mn – 24n^{2}

Factorise the following:

`sqrt(5)"a"^2 + 2"a" - 3sqrt(5)`

Factorise the following:

a^{4} – 3a^{2} + 2

Factorise the following:

8m^{3} – 2m^{2}n – 15mn^{2}

Factorise the following:

`1/x^2 + 1/y^2 + 2/(xy)`

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 3 Algebra Exercise 3.7 [Pages 111 - 112]

Find the quotient and remainder of the following.

(4x^{3} + 6x^{2} – 23x + 18) ÷ (x + 3)

Find the quotient and remainder of the following.

(8y^{3} – 16y^{2} + 16y – 15) ÷ (2y – 1)

Find the quotient and remainder of the following.

(8x^{3} – 1) ÷ (2x – 1)

Find the quotient and remainder of the following.

(−18z + 14z^{2} + 24z^{3} + 18) ÷ (3z + 4)

The area of a rectangle is x^{2} + 7x + 12. If its breadth is (x + 3), then find its length

The base of a parallelogram is (5x + 4). Find its height if the area is 25x^{2} – 16

The sum of (x + 5) observations is (x^{3} + 125). Find the mean of the observations

Find the quotient and remainder for the following using synthetic division:

(x^{3} + x^{2} – 7x – 3) ÷ (x – 3)

Find the quotient and remainder for the following using synthetic division:

(x^{3} + 2x^{2} – x – 4) ÷ (x + 2)

Find the quotient and remainder for the following using synthetic division:

(3x^{3} – 2x^{2} + 7x – 5) ÷ (x + 3)

Find the quotient and remainder for the following using synthetic division:

(8x^{4} – 2x^{2} + 6x + 5) ÷ (4x + 1)

If the quotient obtained on dividing (8x^{4} – 2x^{2} + 6x – 7) by (2x + 1) is (4x^{3} + px^{2} – qx + 3), then find p, q and also the remainder

If the quotient obtained on dividing 3x^{3} + 11x^{2} + 34x + 106 by x – 3 is 3x^{2} + ax + b, then find a, b and also the remainder

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 3 Algebra Exercise 3.8 [Page 114]

Factorise the following polynomials using synthetic division:

x^{3} – 3x^{2} – 10x + 24

Factorise the following polynomials using synthetic division:

2x^{3} – 3x^{2} – 3x + 2

Factorise the following polynomials using synthetic division:

– 7x + 3 + 4x^{3}

Factorise the following polynomials using synthetic division:

x^{3} + x^{2} – 14x – 24

Factorise the following polynomials using synthetic division:

x^{3} – 7x + 6

Factorise the following polynomials using synthetic division:

x^{3} – 10x^{2} – x + 10

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 3 Algebra Exercise 3.9 [Page 115]

Find the G.C.D for the following:

P^{5}, P^{11}, P^{9}

Find the G.C.D for the following:

4x^{3}, y^{3}, z^{3}

Find the G.C.D for the following:

9a^{2}b^{2}c^{3}, 15a^{3}b^{2}c^{4}

Find the G.C.D for the following:

64x^{8}, 240x^{6}

Find the G.C.D for the following:

ab^{2}c^{3}, a^{2}b^{3}c, a^{3}bc^{2}

Find the G.C.D for the following:

35x^{5}y^{3}z^{4}, 49x^{2}yz^{3}, 14xy^{2}z^{2}

Find the G.C.D for the following:

25ab^{3}c, 100a^{2}bc, 125ab

Find the G.C.D for the following:

3abc, 5xyz, 7pqr

Find the G.C.D of the following:

(2x + 5), (5x + 2)

Find the G.C.D of the following:

a^{m+1}, a^{m+2}, a^{m+3 }

Find the G.C.D of the following:

2a^{2 }+ a, 4a^{2} – 1

Find the G.C.D of the following:

3a^{2}, 5b^{3}, 7c^{4 }

Find the G.C.D of the following:

x^{4} – 1, x^{2} – 1

Find the G.C.D of the following:

a^{3} – 9ax^{2}, (a – 3x)^{2}

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 3 Algebra Exercise 3.10 [Page 124]

Draw the graph for the following

y = 2x

Draw the graph for the following

y = 4x – 1

Draw the graph for the following

y = `(3/2)x + 3`

Draw the graph for the following

3x + 2y = 14

Solve graphically

x + y = 7, x – y = 3

Solve graphically

3x + 2y = 4, 9x + 6y – 12 = 0

Solve graphically

`x/2 + y/4` = 1, `x/2 + y/4` = 2

Solve graphically

x – y = 0, y + 3 = 0

Solve graphically

y = 2x + 1, y + 3x – 6 = 0

Solve graphically

x = −3, y = 3

Two cars are 100 miles apart. If they drive towards each other they will meet in 1 hour. If they drive in the same direction they will meet in 2 hours. Find their speed by using graphical method.

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 3 Algebra Exercise 3.11 [Page 126]

Solve, using the method of substitution

2x – 3y = 7, 5x + y = 9

Solve, using the method of substitution

1.5x + 0.1y = 6.2, 3x – 0.4y = 11.2

Solve, using the method of substitution

10% of x + 20% of y = 24, 3x – y = 20

Solve, using the method of substitution

`sqrt(2)x - sqrt(3)y` = 1, `sqrt(3)x - sqrt(8)y` = 0

Raman’s age is three times the sum of the ages of his two sons. After 5 years his age will be twice the sum of the ages of his two sons. Find the age of Raman.

The middle digit of a number between 100 and 1000 is zero and the sum of the other digit is 13. If the digits are reversed, the number so formed exceeds the original number by 495. Find the number

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 3 Algebra Exercise 3.12 [Page 128]

Solve by the method of elimination

2x – y = 3, 3x + y = 7

Solve by the method of elimination

x – y = 5, 3x + 2y = 25

Solve by the method of elimination

`x/10 + y/5` = 14, `x/8 + y/6` = 15

Solve by the method of elimination

3(2x + y) = 7xy, 3(x + 3y) = 11xy

Solve by the method of elimination

`4/x + 5y` = 7, `3/x + 4y` = 5

Solve by the method of elimination

13x + 11y = 70, 11x + 13y = 74

The monthly income of A and B are in the ratio 3 : 4 and their monthly expenditures are in the ratio 5 : 7. If each saves ₹ 5,000 per month, find the monthly income of each

Five years ago, a man was seven times as old as his son, while five year hence, the man will be four times as old as his son. Find their present age

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 3 Algebra Exercise 3.13 [Page 131]

Solve by cross-multiplication method

8x – 3y = 12, 5x = 2y + 7

Solve by cross-multiplication method

6x + 7y – 11 = 0, 5x + 2y = 13

Solve by cross-multiplication method

`2/x + 3/y` = 5, `3/x - 1/y + 9` = 0

Akshaya has 2 rupee coins and 5 rupee coins in her purse. If in all she has 80 coins totalling ₹ 220, how many coins of each kind does she have.

It takes 24 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 8 hours and the pipe of the smaller diameter is used for 18 hours. Only half of the pool is filled. How long would each pipe take to fill the swimming pool

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 3 Algebra Exercise 3.14 [Page 133]

#### Solve by anyone of the methods

The sum of a two digit number and the number formed by interchanging the digits is 110. If 10 is subtracted from the first number, the new number is 4 more than 5 times the sums of the digits of the first number. Find the first number.

The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes `1/2`. Find the fraction

ABCD is a cyclic quadrilateral such that ∠A = (4y + 20)°, ∠B = (3y − 5)°, ∠C = (4x)° and ∠D = (7x + 5)°. Find the four angles

On selling a T.V. at 5% gain and a fridge at 10% gain, a shopkeeper gains ₹ 2000. But if he sells the T.V. at 10% gain and the fridge at 5% loss, he gains Rs. 1500 on the transaction. Find the actual price of the T.V. and the fridge.

Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5. Find the numbers.

4 Indians and 4 Chinese can do a piece of work in 3 days. While 2 Indians and 5 Chinese can finish it in 4 days. How long would it take for 1 Indian to do it? How long would it take for 1 Chinese to do it?

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 3 Algebra Exercise 3.15 [Pages 134 - 136]

#### Multiple choice questions

If x^{3} + 6x^{2} + kx + 6 is exactly divisible by (x + 2), then k = ?

−6

−7

−8

11

The root of the polynomial equation 2x + 3 = 0 is

`1/3`

`-1/3`

`-3/2`

`-2/3`

The type of the polynomial 4 – 3x^{3} is

constant polynomial

linear polynomial

quadratic polynomial

cubic polynomial

If x^{51} + 51 is divided by x + 1, then the remainder is

0

1

49

50

The zero of the polynomial 2x + 5 is

`5/2`

`-5/2`

`2/5`

`-2/5`

The sum of the polynomials p(x) = x^{3} – x^{2} – 2, q(x) = x^{2} – 3x + 1

x

^{3}– 3x – 1x

^{3}+ 2x^{2}– 1x

^{3}– 2x^{2}– 3xx

^{3}– 2x^{2}+ 3x – 1

Degree of the polynomial (y^{3 }– 2)(y^{3} + 1) is

9

2

3

6

Let the polynomials be**(A)** −13q^{5} + 4q^{2 }+ 12q

**(B)** (x^{2} + 4)(x^{2} + 9)

**(C)** 4q^{8} – q^{6} + q^{2}

**(D)** `– 5/7 y^12 + y^3 + y^5`^{ }

Then ascending order of their degree is

A, B, D, C

A, B, C, D

B, C, D, A

B, A, C, D

If p(a) = 0 then (x – a) is a ___________ of p(x)

divisor

quotient

remainder

factor

Zeros of (2 – 3x) is ___________

3

2

`2/3`

`3/2`

Which of the following has x – 1 as a factor?

2x – 1

3x – 3

4x – 3

3x – 4

If x – 3 is a factor of p(x), then the remainder is

3

– 3

p(3)

p(–3)

(x + y)(x^{2} – xy + y^{2}) is equal to

(x + y)

^{3}(x – y)

^{3}x

^{3}+ y^{3}x

^{3}– y^{3}

(a + b – c)^{2} is equal to __________

(a – b + c)

^{2}(–a – b + c)

^{2}(a + b + c)

^{2}(a – b – c)

^{2}

If (x + 5) and (x – 3) are the factors of ax^{2} + bx + c, then values of a, b and c are

1, 2, 3

1, 2, 15

1, 2, −15

1, −2, 15

Cubic polynomial may have maximum of ___________ linear factors

1

2

3

4

Degree of the constant polynomial is __________

3

2

1

0

Find the value of m from the equation 2x + 3y = m. If its one solution is x = 2 and y = −2

2

− 2

10

0

Which of the following is a linear equation?

`x + 1/x` = 2

x(x – 1) = 2

3x + 5 = `2/3`

x

^{3}– x = 5

Which of the following is a solution of the equation 2x – y = 6?

(2, 4)

(4, 2)

(3, −1)

(0, 6)

If (2, 3) is a solution of linear equation 2x + 3y = k then, the value of k is

12

6

0

13

Which condition does not satisfy the linear equation ax + by + c = 0

a ≠ 0, b = 0

a = 0, b ≠ 0

a = 0, b = 0, c ≠ 0

a ≠ 0, b ≠ 0

Which of the following is not a linear equation in two variable

ax + by + c = 0

0x + 0y + c = 0

0x + by + c = 0

ax + 0y + c = 0

The value of k for which the pair of linear equations 4x + 6y – 1 = 0 and 2x + ky – 7 = 0 represents parallel lines is

k = 3

k = 2

k = 4

k = − 3

A pair of linear equations has no solution then the graphical representation is

If `"a"_1/"a"_2 ≠ "b"_1/"b"_2` where a_{1}x + b_{1}y + c_{1} = 0 and a_{2}x + b_{2}y + c_{2} = 0 then the given pair of linear equation has __________ solution(s)

no solution

two solutions

unique

infinite

If `"a"_1/"a"_2 = "b"_1/"b"_2 ≠ "c"_1/"c"_2` where a_{1}x + b_{1}y + c_{1} = 0 and a_{2}x + b_{2}y + c_{2} = 0 then the given pair of linear equation has __________ solution(s)

no solution

two solutions

infinite

unique

G.C.D of any two prime numbers is __________

−1

0

1

2

The G.C.D of x^{4} – y^{4} and x^{2} – y^{2} is

x

^{4}– y^{4}x

^{2}– y^{2}(x + y)

^{2}(x + y)

^{4}

## Chapter 3: Algebra

## Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board chapter 3 - Algebra

Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board chapter 3 (Algebra) 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 Tamil Nadu Board of Secondary Education Mathematics Class 9th Tamil Nadu State Board solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Samacheer Kalvi textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Mathematics Class 9th Tamil Nadu State Board chapter 3 Algebra are Concept of Polynomials, Algebraic Expressions, Value of a Polynomial, Roots of a Polynomial Equation, Concept of Identity, Polynomials in One Variable, Standard Form of a Polynomial, Degree of Polynomial, Remainder Theorem, Expansion of (a + b)2 = a2 + 2ab + b2, Expansion of (a - b)2 = a2 - 2ab + b2, Expansion of (a + b)(a - b), Types of Polynomials, Expansion of (x + a)(x + b), Arithmetic of Polynomials, Factor Theorem, Addition of Polynomials, Subtraction of Polynomials, Multiplication of Two Polynomials, Expansion of (a + b + c)2, Synthetic Division, Expansion of (x + a)(x + b)(x + c), Expansion of (a + b)3, Expansion of (a - b)3, Factorisation Using Identities, Highest Common Factor, Factorisation Using Identity a2 + 2ab + b2 = (a + b)2, Factorisation Using Identity a2 - 2ab + b2 = (a - b)2, Factorisation Using Identity a2 - b2 = (a + b)(a - b), General Form of Linear Equation in Two Variables, Factorisation using Identity a2 + b2 + c2 + 2ab + 2bc + 2ac = (a + b + c)2, Graph of a Linear Equation in Two Variables, Factorisation using Identity a3 + b3 = (a + b)(a2 - ab + b2), Factorisation using Identity a3 - b3 = (a - b)(a2 + ab + b2), Factorisation using Identity a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca), Factorising the Quadratic Polynomial (Trinomial) of the type ax2 + bx + c, a ≠ 0., Division Algorithm for Polynomials, Simultaneous Linear Equations, Methods of Solving Simultaneous Linear Equations by Graphical Method, Methods of Solving Simultaneous Linear Equations by Substitution, Methods of Solving Simultaneous Linear Equations by Cross Multiplication Method, Methods of Solving Simultaneous Linear Equations by Elimination Method, Comparing the Ratios of Coefficients of a Linear Equation, Consistency and Inconsistency of Linear Equations in Two Variables, Zeroes of a Polynomial.

Using Samacheer Kalvi Class 9th solutions Algebra exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Samacheer Kalvi Solutions are important questions that can be asked in the final exam. Maximum students of Tamil Nadu Board of Secondary Education Class 9th prefer Samacheer Kalvi Textbook Solutions to score more in exam.

Get the free view of chapter 3 Algebra Class 9th extra questions for Mathematics Class 9th Tamil Nadu State Board and can use Shaalaa.com to keep it handy for your exam preparation