#### Chapters

Chapter 2 - Polynomials

Chapter 3 - Coordinate Geometry

Chapter 4 - Linear Equations in two Variables

Chapter 5 - Introduction to Euclid's Geometry

Chapter 6 - Lines and Angles

Chapter 7 - Triangles

Chapter 8 - Quadrilaterals

Chapter 9 - Areas of Parallelograms and Triangles

Chapter 10 - Circles

Chapter 11 - Constructions

Chapter 12 - Heron's Formula

Chapter 13 - Surface Area and Volumes

Chapter 14 - Statistics

Chapter 15 - Probability

## Chapter 2 - Polynomials

#### Page 32

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

`(i) 4x^2 - 3x + 7`

`(ii) y^2+sqrt2`

`(iii) 3sqrtt+tsqrt2`

`(iv) y+2/y`

`(v) x^10+y^3+t^50`

Write the coefficients of x^{2} in each of the following:-

`(i) 2+x^2+x`

`(ii) 2-x^2+x^3`

`(iii) pi/2x^2+x`

`(iv) sqrt2x-1`

Give one example each of a binomial of degree 35, and of a monomial of degree 100.

Write the degree of each of the following polynomials:-

(i) 5x^{3} + 4x^{2} +7x

(ii) 4 - y^{2}

`(iii) 5t - sqrt7`

(iv) 3

Classify the following as linear, quadratic and cubic polynomials:-

(i) x^{2} + x

(ii) x – x^{3}

(iii) y + y^{2} + 4

(iv) 1 + x

(v) 3t

(vi) r^{2}

(vii) 7x^{3}

#### Pages 34 - 35

Find the value of the polynomial 5x – 4x^{2} + 3 at

(i) x = 0

(ii) x = –1

(iii) x = 2

Find p(0), p(1) and p(2) for the following polynomials:-

p(y) = y^{2} – y + 1

Find p(0), p(1) and p(2) for the following polynomials:-

p(t) = 2 + t + 2t^{2} – t^{3}

Find p(0), p(1) and p(2) for the following polynomials:-

p(x) = x^{3}

Find p(0), p(1) and p(2) for the following polynomials:-

p(x) = (x – 1) (x + 1)

Verify whether the following zeroes of the polynomial, indicated against them.

p(x) = 3x + 1, x =-1/3

Verify whether the following zeroes of the polynomial, indicated against them.

p(x) = 5x – π, x = 4/5

Verify whether the following zeroes of the polynomial, indicated against them.

p(x) = x^{2} – 1, x = 1, –1

Verify whether the following zeroes of the polynomial, indicated against them.

p(x) = (x + 1) (x – 2), x = – 1, 2

Verify whether the following zeroes of the polynomial, indicated against them.

p(x) = x^{2}, x = 0

Verify whether the following zeroes of the polynomial, indicated against them.

p(x) = lx + m, `x = – m/l`

Verify whether the following zeroes of the polynomial, indicated against them.

`p(x) = 3x^2 – 1, x = -1/sqrt3,2/sqrt3`

Verify whether the following zeroes of the polynomial, indicated against them.

p(x) = 2x + 1, x = 1/2

Find the zero of the polynomial in the following case:- p(x) = x + 5

Find the zero of the polynomial in the following case:- p(x) = x – 5

Find the zero of the polynomial in the following case:- p(x) = 3x – 2

Find the zero of the polynomial in the following case:- p(x) = 2x + 5

Find the zero of the polynomial in the following case:- p(x) = 3x

Find the zero of the polynomial in the following case:-

p(x) = ax, a ≠ 0

Find the zero of the polynomial in the following case:- p(x) = cx + d, c ≠ 0, c, d are real numbers.

#### Page 40

Find the remainder when x^{3} + 3x^{2} + 3x + 1 is divided by x+1.

Find the remainder when x^{3} + 3x^{2} + 3x + 1 is divided by `x - 1/2`

Find the remainder when x^{3} + 3x^{2} + 3x + 1 is divided by x.

Find the remainder when x^{3} + 3x^{2} + 3x + 1 is divided by x + π.

Find the remainder when x^{3} + 3x^{2} + 3x + 1 is divided by 5 + 2x.

Find the remainder when x^{3} – ax^{2} + 6x – a is divided by x – a.

Check whether 7 + 3x is a factor of 3x^{3} + 7x.

#### Page 44

Determine which of the following polynomials has (x + 1) a factor :-

(i) *x*^{3} + *x*^{2} + *x* + 1

(ii) *x*^{4} + *x*^{3} + *x*^{2} + *x* + 1

(iii) *x*^{4} + 3*x*^{3} + 3*x*^{2} + *x* + 1

`(iv) x^3-x^2-(2+sqrt2)x+sqrt2`

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:-

p(x) = 2x^{3} + x^{2} – 2x – 1, g(x) = x + 1

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:-

*p*(*x*) = *x*^{3} + 3*x*^{2} + 3*x* + 1, *g*(*x*) = *x* + 2

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:-

*p*(*x*) = *x*^{3} − 4*x*^{2} + *x* + 6, *g*(*x*) = *x* − 3

Find the value of k, if x – 1 is a factor of p(x) in the following case:- p(x) = x^{2} + x + k

Find the value of k, if x – 1 is a factor of p(x) in the following case:-

`p(x) = 2x^2+kx+sqrt2`

Find the value of k, if x – 1 is a factor of p(x) in the following case:- `p(x) = kx^2 - sqrt2x +1`

Find the value of k, if x – 1 is a factor of p(x) in the following case:-

p(x) = kx^{2} – 3x + k

Factorise :- 12x^{2} – 7x + 1

Factorise :- 2x^{2} + 7x + 3

Factorise :- 6x^{2} + 5x – 6

Factorise :- 3x^{2} – x – 4

Factorise :- x^{3} – 2x^{2} – x + 2

Factorise :- x^{3} – 3x^{2} – 9x – 5

Factorise :- x^{3} + 13x^{2} + 32x + 20

Factorise :- 2y^{3} + y^{2} – 2y – 1