Polynomial
Basics Revisited
Algebraic Expressions
An algebraic expression is an expression made up of variables and constants along with
mathematical operators.
An algebraic expression is a sum of terms, which are considered to be building blocks
for expressions.
A term is a product of variables and constants. A term can be an algebraic expression in
itself.
Examples of a term - 3 which is just a constant.
- 2x, which is the product of constant '2' and the variable 'x'
- 4xy, which is the product of the constant '4' and the variables 'x' and 'y'.
- 5x y, which is the product of 5, x, x and y.
2
The constant in each term is referred to as the coefficient .
Example of an algebraic expression - 3x 2
y + 4xy + 5x + 6 - which is the sum of four terms -
2
3x y, 4xy, 5x and 6
An algebraic expression can have any number of terms. The coefficient in each term can be
any real number. There can be any number of variables in an algebraic expression. The
exponent on the variables, however, must be rational numbers.
Polynomial
An algebraic expression can have exponents that are rational numbers. However, a
polynomial is an algebraic expression in which the exponent on any variable is a whole
number.
5x
3
+ 3x + 1 is an example of a polynomial. It is an algebraic expression as well
2x + 3√x is an algebraic expression, but not a polynomial. - since the exponent on x is 1
2
which is not a whole number.
Degree of a Polynomial
For a polynomial in one variable - the highest exponent on the variable in a polynomial is
the degree of the polynomial.
, Example: The degree of the polynomial x 2
+ 2x + 3 is 2, as the highest power of x in the
given expression is x . 2
TYPES OF POLYNOMIALS
Polynomials can be classified based on
a) Number of terms
b) Degree of the polynomial.
Types of polynomials based on the number of terms
a) Monomial - A polynomial with just one term. Example - 2x, 6x , 9xy 2
b) Binomial - A polynomial with two terms. Example - 4x 2
+ x , 5x + 4
a) Trinomial - A polynomial with three terms. Example - x 2
+ 3x + 4
Types of polynomials based on degree:
Linear Polynomial
A polynomial whose degree is one is called a linear polynomial.
For example, 2x + 1 is a linear polynomial.
Quadratic Polynomial
A polynomial of degree two is called a quadratic polynomial.
For example, 3x 2
+ 8x + 5 is a quadratic polynomial.
Cubic Polynomial
A polynomial of degree three is called a cubic polynomial.
For example, 2x 3
+ 5x
2
+ 9x + 15 is a cubic polynomial.
Graphical Representations
Representing Equations on a Graph
Basics Revisited
Algebraic Expressions
An algebraic expression is an expression made up of variables and constants along with
mathematical operators.
An algebraic expression is a sum of terms, which are considered to be building blocks
for expressions.
A term is a product of variables and constants. A term can be an algebraic expression in
itself.
Examples of a term - 3 which is just a constant.
- 2x, which is the product of constant '2' and the variable 'x'
- 4xy, which is the product of the constant '4' and the variables 'x' and 'y'.
- 5x y, which is the product of 5, x, x and y.
2
The constant in each term is referred to as the coefficient .
Example of an algebraic expression - 3x 2
y + 4xy + 5x + 6 - which is the sum of four terms -
2
3x y, 4xy, 5x and 6
An algebraic expression can have any number of terms. The coefficient in each term can be
any real number. There can be any number of variables in an algebraic expression. The
exponent on the variables, however, must be rational numbers.
Polynomial
An algebraic expression can have exponents that are rational numbers. However, a
polynomial is an algebraic expression in which the exponent on any variable is a whole
number.
5x
3
+ 3x + 1 is an example of a polynomial. It is an algebraic expression as well
2x + 3√x is an algebraic expression, but not a polynomial. - since the exponent on x is 1
2
which is not a whole number.
Degree of a Polynomial
For a polynomial in one variable - the highest exponent on the variable in a polynomial is
the degree of the polynomial.
, Example: The degree of the polynomial x 2
+ 2x + 3 is 2, as the highest power of x in the
given expression is x . 2
TYPES OF POLYNOMIALS
Polynomials can be classified based on
a) Number of terms
b) Degree of the polynomial.
Types of polynomials based on the number of terms
a) Monomial - A polynomial with just one term. Example - 2x, 6x , 9xy 2
b) Binomial - A polynomial with two terms. Example - 4x 2
+ x , 5x + 4
a) Trinomial - A polynomial with three terms. Example - x 2
+ 3x + 4
Types of polynomials based on degree:
Linear Polynomial
A polynomial whose degree is one is called a linear polynomial.
For example, 2x + 1 is a linear polynomial.
Quadratic Polynomial
A polynomial of degree two is called a quadratic polynomial.
For example, 3x 2
+ 8x + 5 is a quadratic polynomial.
Cubic Polynomial
A polynomial of degree three is called a cubic polynomial.
For example, 2x 3
+ 5x
2
+ 9x + 15 is a cubic polynomial.
Graphical Representations
Representing Equations on a Graph
