Theory:

The polynomial degree is the highest variable power in a polynomial.
p(x)=9x3 3x2 +8x  2. In this polynomial, the highest variable power is \(3\).
 
p(x)=3x2 +8x  2. In this polynomial, the highest variable power is \(2\).
 
Polynomial classification based on degree:
  • Linear Polynomial: A polynomial of degree \(1\) — p(x)=8x – 2.
  • Quadratic Polynomial: A polynomial of degree \(2\) — p(x)=3x2+8x  2.
  • Cubic Polynomial: A polynomial of degree \(3\) — p(x)=9x33x2+8x2.
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)=ax2+bx+c.
  • Cubic Polynomial: A polynomial in one variable with degree three is called a cubic polynomial. It is denoted as p(x)=ax3+bx2+cx+d.
Important!
It's not defined the degree of zero polynomial. There can be any degree. p(x)=0 can be substituted as p(x)=0×xn — where '\(n\)' can be any number.
 
For example: \(p(x) = 0 × x^6 = 0\).
 
The constant polynomial is the form \(p(x) = c\), where \(c\) is the actual number. This means that it is constant for all possible values of \(x\), \(p(x) = c\).

For example: \(p(x) = 6 = 6 x^0\) [where \(x^0 = 1\)]
 
Note that the highest power of the '\(x\)' is zero.
 
Therefore, the degree of the non-zero constant polynomial is zero.