Classifying Polynomials

Classifying Polynomials

Degree of a Polynomial

• The degree of a polynomial is the highest power of the variable (usually x) in the polynomial.
• The degree of a polynomial can be used to classify polynomials into different types.
• For example, a polynomial with a degree of 2 is a quadratic polynomial, while a polynomial with a degree of 3 is a cubic polynomial.

Monomials

• A monomial is a polynomial with only one term.
• Examples of monomials include:
  • 3x^2
  • 2x^3
  • 5x
• The degree of a monomial is the power of the variable in the term.

Binomials

• A binomial is a polynomial with two terms.
• Examples of binomials include:
  • x^2 + 3x
  • 2x^2 - 4
  • x + 2
• Binomials can be factored into the product of two binomials.

Trinomials

• A trinomial is a polynomial with three terms.
• Examples of trinomials include:
  • x^2 + 2x + 1
  • x^3 - 2x^2 - x
  • x^2 - 4x + 4
• Trinomials can be factored into the product of three binomials.

Standard Form

• A polynomial in standard form is written in the order of decreasing powers of the variable.
• For example, the polynomial x^3 + 2x^2 - 3x + 1 is in standard form.
• The standard form of a polynomial can be used to easily identify the degree of the polynomial and to add and subtract polynomials.

Learn about the different types of polynomials, including monomials, binomials, and trinomials, and how to identify their degree and standard form.