Different types of polynomials

Introduction:-

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 coefficients 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 degree .The 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.

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