Math Antics: Introduction to Polynomials

Key Concepts

• Polynomials: A concept in Algebra involving mathematical expressions called "terms."
• Terms: Composed of two parts:
  • Coefficient: The number part of a term (e.g., 2, 5, 1.4).
  • Variable Part: One or more variables raised to a power (e.g., x², y).

Writing Terms

• Terms are written without a multiplication symbol (e.g., 6y rather than y6).
• Number part is conventionally written first.

Understanding Polynomials

• Polynomial: A chain of terms linked by addition or subtraction.
  • Can contain any number of terms.
  • Monomial: One term.
  • Binomial: Two terms.
  • Trinomial: Three terms.
  • Beyond three terms, generally referred to as "polynomial."

Example of a Polynomial

• Example: 3x² + x - 5.
  • Has three terms: 3x², x (implied coefficient of 1), -5 (constant term).

Degree of Terms and Polynomials

• Degree of a Term: Determined by the power of the variable.
  • 4th degree: power of 4, 3rd degree: power of 3, etc.
  • Terms with no variable part are "zero degree" or "constant terms."
• Degree of Polynomials: Determined by the highest degree term.
  • Arranged from highest to lowest degree.
  • Example: "4x to the fifth" should be written first.

Handling Positive and Negative Coefficients

• Treat minus signs as negative signs for the coefficient.
• All terms are added, each with a positive or negative coefficient.
• Important for rearranging polynomials without changing their value.

Conclusion

• Understanding polynomials involves recognizing terms, coefficients, variable parts, and arranging by degree.
• It's crucial to identify positive and negative terms for simplifying polynomials.
• Practice and review are recommended to fully grasp the concepts.