Degree of a Polynomial

Degree of a Polynomial

The degree of a polynomial is the highest power of the variable (usually x) in the polynomial.

Key Points:

• The degree of a polynomial is a non-negative integer.
• The degree of a polynomial is the largest exponent of the variable in the polynomial.
• A polynomial with degree 0 is a constant polynomial.
• A polynomial with degree 1 is a linear polynomial.
• A polynomial with degree 2 is a quadratic polynomial.
• A polynomial with degree 3 is a cubic polynomial.

Examples:

• The polynomial 3x^4 + 2x^2 - 5 has a degree of 4, because the highest power of x is 4.
• The polynomial x^2 - 4x + 2 has a degree of 2, because the highest power of x is 2.
• The polynomial 5 has a degree of 0, because it is a constant polynomial.

Importance of Degree:

• The degree of a polynomial determines the number of roots or solutions it can have.
• The degree of a polynomial also determines the shape of its graph.
• Polynomials of different degrees have different properties and behaviors.

Degree of a Polynomial

• The degree of a polynomial is the highest power of the variable (usually x) in the polynomial.

Key Points

• The degree of a polynomial is a non-negative integer.
• The degree of a polynomial is the largest exponent of the variable in the polynomial.
• Polynomials can have different degrees, including:
  • 0, which is a constant polynomial.
  • 1, which is a linear polynomial.
  • 2, which is a quadratic polynomial.
  • 3, which is a cubic polynomial.

Examples

• The highest power of x in the polynomial 3x^4 + 2x^2 - 5 is 4, making its degree 4.
• The highest power of x in the polynomial x^2 - 4x + 2 is 2, making its degree 2.
• The polynomial 5 has a degree of 0, because it is a constant polynomial.

Importance of Degree

• A polynomial's degree determines the number of roots or solutions it can have.
• The degree of a polynomial determines the shape of its graph.
• Polynomials of different degrees have different properties and behaviors.