POLYNOMIALS(Algebra)

Class – 10Mathematics

Synopsis

• Meaning of polynomial• Examples of polynomial• Examples of non polynomial• Degree of polynomial• Types of polynomial• General form of polynomial• Value of a polynomial at a given point

Meaning - Polynomial

• It is an expression made with constants, variables and exponents which are combined using addition, subtraction and multiplication but not division.

• The exponents can only be 0,1,2,3....etc

• A polynomial cannot have infinite number of terms.

Examples of polynomial

3535 32 YXXY

13456 234 xxxx

53 x

Examples of non polynomial

23 xx

22x

2x

Degree of a polynomial

Highest power of x in P(x). For example:4x+2 is a polynomial in the variable x of degree 1

Tell the degree of the following polynomials;

Answer is 3 because it is the highest degree of the given polynomial.

1234 23 xxx

Types of polynomials

On the basis of degree we have mainly 5 types:1. Constant polynomial of degree 0, for instance:

2. Linear polynomial of degree 1, for instance:

3. Quadratic polynomial of degree 2, for instance

132

u

vvyxx325,2,

5232 222

2x-3, y+2,

1, 2/5, -3

Types of polynomials4. Cubic Polynomial of degree 3, for instance:

5. Bi –quadratic polynomial of degree 4, for instance:

323 3,2 xxx

582 34 xxx

Types of polynomialOn the basis of number of terms, we have 3 types ofpolynomials1. Monomial polynomial wherein only one term exist:

2. Binomial polynomial where only 2 terms exists:

3. Trinomial polynomial where 3 terms exists:

53,257 2 xx

523 2 xx

yx32,7

General form of polynomial

• Linear polynomial:

• Quadratic polynomial:

• Cubic polynomial:

0, abax

0,2 acbxax

0,23 adcxbxax

Value of a polynomial at a given point

If p(x) is a polynomial in x and a is real number. Then the value obtained by putting x=a in p(x) is called the value of p(x) at x=a.

Let its value at x=2 is

Thus, 14 is the value.

245)( 2 xxxp

142820)2(2)2(4)2(5)2( 2

pp

Lesson by:

Anjali Kaur SuriTGT Maths, PGT Economics

M.A. (Economics), M.Com (Finance), PGD Banking & Finance, B.A. Hons (Economics), B.Ed (Maths & SST), NISM, NSDL and IELTS certified.

For enquiries, email contact@geniusedu.co.in