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.