Chapter 2 POLYNOMIALS THEORY

Question 1

Algebraic expressions?

Answer 1

Combination of constants and variables, connected by some or all the basic arithmetic operations+,-,×,÷.

Question 2

Constant?

Answer 2

A symbol having fixed numerical value

Question 3

Variable?

Answer 3

A symbol which maybe assigned different numerical values,or a symbol which can have varying numerical value

Question 4

Polynomial?

Answer 4

An algebraic expressions in which the variables involved only non negative integral (whole numbers) exponents

Question 5

Terms of a polynomial?

Answer 5

Several non zero parts of polynomial separated by + or - operations are called the terms of the polynomial.

Question 6

Coefficients of the terms of a polynomial?

Answer 6

Each term of a polynomial has some constant multiplied to the variable,it is known as the coefficient of the variable

Question 7

Standard form of polynomial?

Answer 7

A polynomial written in ascending/descending powers of the variable

Question 8

Monomial?

Answer 8

A polynomial having only one term

Question 8

Binomial?

Answer 8

Polynomial having 2 terms

Question 9

Trinomial?

Answer 9

A polynomial having 3 terms.

Question 10

Degree of a polynomial?

Answer 10

Highest exponents of the variable is known as the degree of the polynomial.

Question 11

Constant polynomial?

Answer 11

A polynomial consisting of only a constant is called a constant polynomial.
Eg:π-6/5

(Every real number is a constant polynomial.)

Question 12

Linear polynomial?

Answer 12

A polynomial of degree 1

Question 13

Quadratic polynomial?

Answer 13

A polynomial of degree 2

Question 14

Cubic polynomial?

Answer 14

A polynomial of degree 3

Question 15

Zero polynomial?

Answer 15

0😝

Question 16

Zeros of a polynomial?

Answer 16

The value of a variable in a polynomial,which can be placed in place of variable and the value comes at zero,then it’s a zeros of a polynomial.

Question 17

How to determine how any zeros will a polynomial will have?

Answer 17

By its highest power(degree)

Question 18

Factorisation?

Answer 18

Process of writing a polynomial as a product of two or more polynomials is called factorisation.

Question 19

Methods of factorisation?

Answer 19

1)taking out the common factor

2) grouping the terms

3)middle the splitting method
That’s it 😺
Just kidding

4) by factor theorem

Question 20

(a + b)²=

Answer 20

a² + 2ab + b²

Question 21

(a – b)² =

Answer 21

a² – 2ab + b²

Question 21

a² – b² =

Answer 21

(a + b)(a – b)

Question 22

(x + a)(x + b) =

Answer 22

x² + (a + b)x + ab

Question 23

(a + b + c)² =

Answer 23

a² + b² + c² + 2ab + 2bc + 2ca

Question 24

x³ + y³ + z³ – 3xyz =

Answer 24

(x + y + z)(x² + y² + z² – xy – yz – zx)

Question 25

x³ + y³ =

Answer 25

(x + y)(x² – xy + y²)

Question 26

x³ – y³ =

Answer 26

(x – y)(x² + xy + y²)