PDF chapter test TRY NOW
The polynomial degree is the highest variable power in a polynomial.
. In this polynomial, the highest variable power is \(3\).
. In this polynomial, the highest variable power is \(2\).
Polynomial classification based on degree:
- Linear Polynomial: A polynomial of degree \(1\) — .
- Quadratic Polynomial: A polynomial of degree \(2\) — .
- Cubic Polynomial: A polynomial of degree \(3\) — .
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 .
- Quadratic Polynomial: A polynomial in one variable with degree two is called a quadratic polynomial. It can be denoted as .
- Cubic Polynomial: A polynomial in one variable with degree three is called a cubic polynomial. It is denoted as .
Important!
It's not defined the degree of zero polynomial. There can be any degree. can be substituted as — 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.
Register for free to see more content