Polynomials

Polynomials in one variable and their degree :

An algebraic expression involving only one variable in which the powers of the variable are non-negative integers, is a polynomial in that variable.

Degree : The highest power of the variable in a polynomial is called its degree.

Examples :

• x + y + xy is a polynomial in x and y whose terms are of degree 1, 1, and 2 So, it is a polynomial of degree 2.
• a2b + ab2+ 3ab + 5 is a polynomial in a and b whose terms are of degree 3, 3, 2 and 0 respectively. So, it is a polynomial of degree 3.

Quadratic polynomial :

A polynomial of degree 2 is called a quadratic polynomial.

Cubic polynomial :

A polynomial of degree 3 is called a cubic polynomial.

For example : a) 6×3 – 5×2 + 2x + 1 b) z3 – 3z + 7 are both cubic polynomials

Constant polynomial :

A polynomial having one term consisting of a constant only is a constant polynomial.

The degree of a constant polynomial is 0.

Thus, 6 is a constant polynomial.

Example

The algebraic expression: x2 + y3 +xy +7 is a polynomial in x and y with degree 2 and 3 respectively

74 - constant polynomial with degree 0

Algebraic Identity