#### Chapters

Chapter 2 - Exponents of Real Numbers

Chapter 3 - Rationalisation

Chapter 4 - Algebraic Identities

Chapter 5 - Factorisation of Algebraic Expressions

Chapter 6 - Factorisation of Polynomials

Chapter 7 - Introduction to Euclid’s Geometry

Chapter 8 - Lines and Angles

Chapter 9 - Triangle and its Angles

Chapter 10 - Congruent Triangles

Chapter 11 - Co-ordinate Geometry

Chapter 12 - Heron’s Formula

Chapter 13 - Linear Equations in Two Variables

Chapter 14 - Quadrilaterals

Chapter 15 - Areas of Parallelograms and Triangles

Chapter 16 - Circles

Chapter 17 - Constructions

Chapter 18 - Surface Areas and Volume of a Cuboid and Cube

Chapter 19 - Surface Areas and Volume of a Circular Cylinder

Chapter 20 - Surface Areas and Volume of A Right Circular Cone

Chapter 21 - Surface Areas and Volume of a Sphere

Chapter 22 - Tabular Representation of Statistical Data

Chapter 23 - Graphical Representation of Statistical Data

Chapter 24 - Measures of Central Tendency

Chapter 25 - Probability

## Chapter 6 - Factorisation of Polynomials

#### Page 0

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

3x^{2} - 4x +15

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

*`y^2 +2sqrt3`*

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

`3sqrtx+sqrt2x`

`x - 4/x`

`x^12+y^3+t^50`

Write the coefficient of x2 in each of the following:

`17 -2x + 7x^2`

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

`9-12x +X^3`

Write the coefficient of x^{2} in each of the following.

`pi/6x^2- 3x+4`

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

`sqrt3x-7`

Write the degrees of each of the following polynomials

`7x3 + 4x2 – 3x + 12`

Write the degrees of each of the following polynomials:

`12-x+2x^3`

Write the degrees of each of the following polynomials:

`5y-sqrt2`

Write the degrees of each of the following polynomials:

`7=7-x^@`

Write the degrees of each of the following polynomials

0

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

`x+x^2 +4`

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

`3x-2`

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

`2x+x^2`

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

`3y`

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

`t^2+1`

Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials

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

Classify the following polynomials as polynomials in one-variable, two variables etc:

`x^2-xy+7y^2`

Classify the following polynomials as polynomials in one-variable, two variables etc:

`x^2-2tx+7t^2-x+t`

Classify the following polynomials as polynomials in one-variable, two variables etc:

`t^3_3t^2+4t-5`

Classify the following polynomials as polynomials in one-variable, two variables etc:

`xy+yx+zx`

Identify polynomials in the following:

`f(x)=4x^3-x^2-3x+7`

Identify polynomials in the following:

`g(x)=2x^3-3x^2+sqrtx-1`

Identify polynomials in the following:

`p(x)=2/3x^3-7/4x+9`

Identify polynomials in the following:

`q(x)=2x^2-3x+4/x+2`

Identify polynomials in the following:

`h(x)=x^4-x^(3/2)+x-1`

Identify polynomials in the following:

`f(x)=2+3/x+4x`

Identify constant, linear, quadratic and cubic polynomials from the following polynomials:

`f(x)=0`

Identify constant, linear, quadratic and cubic polynomials from the following polynomials:

`g(x)=2x^3-7x+4`

Identify constant, linear, quadratic and cubic polynomials from the following polynomials:

`h(x)=-3x+1/2`

Identify constant, linear, quadratic and cubic polynomials from the following polynomials

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

Identify constant, linear, quadratic and cubic polynomials from the following polynomials:

`q(x)=4x+3`

Identify constant, linear, quadratic and cubic polynomials from the following polynomials:

`r(x)=3x^2+4x^2+5x-7`

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

#### Page 0

If `f(x)=2x^2-13x^2+17x+12` find `f(2)`

If `f(x)=2x^2-13x^2+17x+12` find `f-(3)`

If `f(x)=2x^2-13x^2+17x+12` find `f(0)`

Verify whether the indicated numbers are zeroes of the polynomials corresponding to them in the following cases:

`f ( x ) = 3x +1, x = - 1/3`

Verify whether the indicated numbers are zeroes of the polynomials corresponding to them in the following cases

`f(x)=x^2- 1,x=1,-1`

Verify whether the indicated numbers are zeroes of the polynomials corresponding to them in the following cases

`g(x)=3x^2-2,` `x=2/sqrt3 2/sqrt3`

Verify whether the indicated numbers are zeroes of the polynomials corresponding to them in the following cases:

`f ( x ) = 5x - pi , x = 4/5`

Verify whether the indicated numbers are zeroes of the polynomials corresponding to them in the following cases:

`f ( x) = x^2and x = 0`

`f(x) = lx + m , x = - m/l`

`f (x) = 2x +1, x = 1/2`

If `x = 2` is a root of the polynomial `f(x) = 2x2 – 3x + 7a` find the value of a.

If `x = −1/2` is a zero of the polynomial `p(x)=8x^3-ax^2 -+2` find the value of a.