Polynomial degree and algebraic expression — lesson. Mathematics State Board, Class 9.

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The polynomial degree is the highest variable power in a polynomial.

$p (x) = {9 x}^{3} - {3 x}^{2} + 8 x - 2$ . In this polynomial, the highest variable power is

$3$ .

$p (x) = {3 x}^{2} + 8 x - 2$ . In this polynomial, the highest variable power is

$2$ .

Polynomial classification based on degree:

Linear Polynomial: A polynomial of degree $1$ — $p (x) = 8 x - 2$ .
Quadratic Polynomial: A polynomial of degree $2$ — $p (x) = {3 x}^{2} + 8 x - 2$ .
Cubic Polynomial: A polynomial of degree $3$ — $p (x) = {9 x}^{3} - {3 x}^{2} + 8 x - 2$ .

Important!

It must be noted that there will be a maximum of

$2$ terms in a linear polynomial,

$3$ terms in quadratic polynomials and

$4$ terms in the cubic polynomial of polynomials in one variable.

General form of polynomials of different degrees:

Linear Polynomial: A polynomial in one variable with degree one is called a linear polynomial. It can be denoted as $p (x) = ax + b$ .
Quadratic Polynomial: A polynomial in one variable with degree two is called a quadratic polynomial. It can be denoted as $p (x) = a x^{2} + bx + c$ .
Cubic Polynomial: A polynomial in one variable with degree three is called a cubic polynomial. It is denoted as $p (x) = a x^{3} + b x^{2} + cx + d$ .