## Title:-

# Different types of polynomials:-

## Introduction:-

# Listen full article:

### Today, in this article I will try to explain the topic Different types of polynomials. Hope this will help on going school students a lot.

## Explanation:-

## What is a polynomial?

### Answer:-

### In Mathematics, a polynomial is an expression which consists one or more terms and co-efficients that take part only the operations of addition, subtraction, multiplication, and positive integer power of variables and integer power will never be a negative one or a fraction,or never be the square root of variables .e.g, x² - x - 6 is a quadratic polynomial of variable x as the degree of the polynomial is 2 (in terms of degree if we consider) again it can be called as trinomial (if we consider its total terms).

## How polynomials can be characterised?

### Answer:- Depending on terms polynomials are characterised in four types

and they are :-

(i) Monomial

(ii) Binomial

(iii) Trinomial

(iv)Quadronomial.

### Again depending on degree polynomials are further divided in four types and they are:-

(i) Zero degree polynomial.

(ii) Linear or one degree polynomial.

(ii) Quadratic or two degree polynomial.

(iii) Cubic or three degree polynomial.

## What is monomial?

### Answer :- The polynomial which contains only one term or a single term is known as monomial.e.g; 2x, 10……..etc.

## What is binomial ?

### Answer:- The polynomial which hasThe polynomial which has two terms is known as binomial. e.g; x + y, 2x -5….etc

## What is trinomial?

### Answer:- A polynomial which has three terms is known as trinomial.e.g; x² +y³ -7,

2x + y + 5

## What is quadronomial?

### Answer:- A polynomial which has four terms is known as quadronomial.e.g; 3y³+ x² - z + p, 5z -3y + x -9 …. etc.

## What is a zero degree polynomial?

### Answer:- A polynomial whose highest power of variables is zero is called a zero degree polynomial.e.g; 2x⁰, x⁰ + 5y⁰ + z⁰ ......etc.

## What is one degree or linear polynomial?

### Answer:- The polynomial whose highest exponent of variable is one is called one degreeThe polynomial whose highest exponent of variable is one is called one degree or linear polynomial.e.g; x + y , 9x + 3y +8 are linear polynomials of two variables…..etc.

## What is two degree or quadratic polynomial?

### Answer:- The polynomial whose highest power of variable or sum of exponents of variables is 2 is known as two degree or quadratic polynomial. e.g; 2x² + x + 3 is a quadratic polynomial of single variable x .

### again,

xy + 5z + 2 is a quadratic polynomial of three variables x,y and z. ∵ The powers of variables of x and y are 1and 1,

Now sum of the powers of variables x and y is = 1+ 1 = 2 , so it is a quadratic polynomial.

## What is Cubic polynomial?

### Answer:- A polynomial whose highest variable's power is three is called a cubic polynomial. e.g; x³ + x² +x + 2 is a cubic polynomial of single variable x

5x²y + xy + z is a cubic polynomial of thre variables x,y and z.

### Now let, us do some problems of polynomials:-

## Find the degree of the following polynomials:-

### (i) 4x² + x + 9 (ii) x³ y² + 7y + m

(iii) x - 3y + 5z

### Answer:- (i) The degree of this poly nomial = 2

Explanation:-As,its highest power of variable x is = 2

(ii) The degree of this polynomial = 3 + 2 = 5

Explanation:- As the highest power of variable x = 3 and highest power of variable y = 3

So its degree is = 3 + 2 = 5

(iii) The degree of this polynomial = 1

Explanation :- The highest exponents of the variables x, y and z are equal and it is 1,

So, degree of this polynomial is = 1

## Find out which of the following expressions are polynomials also write their name.

### (i) 1/x + y -7 (ii) y²/³ + 9x + 4 (iii) x³ + y² + z

### Answer:- (i) It is not a polynomial.

Explanation:- The exponent of variable x is = - 1 which is a negative integer.

So, it is not a polynomial.

(ii) It is not a polynomial.

Explanation:- The exponent of variable y is = ⅔ which is a fraction, so it is not a polynomial.

(iii) It is a cubic polynomial ( If we consider its degree)

It is also a trinomial.(If we consider its terms)

Explanation:-

If we consider degree,

Its highest exponent of variable x is = 3 , so it is a cubic polynomial.

Again if we consider terms,

The total number of terms of the expression is = 3

So, it is a trinomial.

## Find a quadratic polynomial

### whose roots are (i) - 2 , 3 (ii) ¼, 4 (iii) 2, 2

### Answer :-

(i) ∵ sum of the roots(s) = - 2 + 3 = 1

and product of the roots (p) = - 2 × 3

= - 6

∴ Quadratic polynomial will be,

x² - sx + p

= x² - 1.x + (- 6)

= x² - x - 6

(ii) ∵ sum of the roots (s) = ¼ + 4/1

= (1 + 16)/4 [ ∵ L.C.M of 1, 4 is 4]

= 17 /4

product of the roots(p) = ¼ × 4

= 1

∴ quadratic equation is,

x² - sx + p = 0

=> x² - 17/4x + 4 = 0

=> 4(x² - 17/4x + 4) = 0 [ multiplying both sides by 4 ]

=> 4x² - 17x + 16 = 0

∴ quadratic polynomial is = 4x² - 17x + 16

## FREQUENTLY ASKED QUESTIONS:-
## What are the four types of polynomial?

Answer :- The four types of polynomials are :-
(i) Monomial:- The polynomial which contains only one term or a single term is known as monomial.e.g; 2x, 10……..etc.
(ii) Binomial :- The polynomial which has two terms is known as binomial. e.g; x + y, 2x -5….etc
( iii) Trinomial :- A polynomial which has three terms is known as trinomial.e.g; x² +y³ -7,
2x + y + 5
(iv) Quadronomial:-A polynomial which has four terms is known as quadronomial.e.g; 3y³+ x² - z + p, 5z -3y + x -9 …. etc

## What is a 6th degree polynomial called?

Answer :- A 6th degree polynomial is called a sextic polynomial.It is also known as hexic polynomial

## What is a zero degree polynomial?

Answer:- A polynomial whose highest power of variables is zero is called a zero degree polynomial.e.g; 2x⁰, x⁰ + 5y⁰ + z⁰ ......etc.

## Is a number a polynomial?

Answer :- Yes, any number is always a polynomial and it is a zero degree polynomial. e.g; 2 is a zero degree polynomial. we can express 2 as,
2 = 2 × 1 = 2.x° = 2x°
So 2 can be called as zero degree polynomial.

##
Which one is a polynomial?
(a)1/(x+y) (b)3x + y -3
(c)√(4m² + 4n²) (d) x⁻³ + 2y² + 3

Answer :- (b)3x + y -3

## What are the four types of polynomial?

Answer :- The four types of polynomials are :- (i) Monomial:- The polynomial which contains only one term or a single term is known as monomial.e.g; 2x, 10……..etc. (ii) Binomial :- The polynomial which has two terms is known as binomial. e.g; x + y, 2x -5….etc ( iii) Trinomial :- A polynomial which has three terms is known as trinomial.e.g; x² +y³ -7, 2x + y + 5 (iv) Quadronomial:-A polynomial which has four terms is known as quadronomial.e.g; 3y³+ x² - z + p, 5z -3y + x -9 …. etc

## What is a 6th degree polynomial called?

Answer :- A 6th degree polynomial is called a sextic polynomial.It is also known as hexic polynomial

## What is a zero degree polynomial?

Answer:- A polynomial whose highest power of variables is zero is called a zero degree polynomial.e.g; 2x⁰, x⁰ + 5y⁰ + z⁰ ......etc.

## Is a number a polynomial?

Answer :- Yes, any number is always a polynomial and it is a zero degree polynomial. e.g; 2 is a zero degree polynomial. we can express 2 as, 2 = 2 × 1 = 2.x° = 2x° So 2 can be called as zero degree polynomial.

## Which one is a polynomial? (a)1/(x+y) (b)3x + y -3 (c)√(4m² + 4n²) (d) x⁻³ + 2y² + 3

Answer :- (b)3x + y -3