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Define the degree of a polynomial with its types
The degree of a polynomial is the highest exponential power of the variable in the polynomial.
Answer: Classification of the polynomials is based on the degree of a polynomial. The degree of a polynomial can be 0, 1, 2, 3, and so on for different polynomials.
Let's explore more about the degree of a polynomial with its types.
Explanation:
The degree of a polynomial is the highest exponential power in the polynomial equation.
Consider the polynomial p(x) : 2x5 − 12x3+ 3x − 6.
The term with the highest power of x is 2x5 and the corresponding (highest) exponent is 5. Therefore, we will say that the degree of this polynomial is 5.
Thus, the degree of a polynomial is the greatest power of a variable in the polynomial equation.
Each of the polynomials has a specific degree and based on that they have been assigned a specific name.
Types of Polynomials | Degree | Examples |
---|---|---|
Constant | 0 | 3 |
Linear | 1 | x + 8 |
Quadratic | 2 | 3x2 - 4x + 9 |
Cubic | 3 | 2x3 + 3x2 + 4x + 6 |
Quartic | 4 | x4- 3x+ 16 |
Quintic | 5 | 4x5+ 2x3 - 20 |
Thus, the degree of a polynomial directly affects the nature of the polynomial expression.
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