Math 102 - Lesson 1: Adding and Subtracting Polynomials

Introduction to Polynomials

• A polynomial is a single term or sum of terms with variables having whole number exponents.
• Written in descending order: highest exponent to the lowest (e.g., (7x^3 - 9x^2 + 13x - 6)).

Important Terms

• Descending Order: Arrangement based on exponents (e.g., (x^3, x^2, x^1)).
• Degree of a Term: The exponent of the term (e.g., in (ax^n), degree = (n)).
• Constant Term: A term without a variable, degree is 0.
• Coefficient: The numerical part of a term (e.g., in (ax^n), coefficient = (a)).

Types of Polynomials

• Monomial: One term (e.g., (2x) or (5x^2)).
• Binomial: Two terms.
• Trinomial: Three terms.
• Polynomials with four or more terms don't get specific names, just called "polynomial."

Degree of a Polynomial

• The degree is the highest degree of its terms.
• Example: For (7x^3 - 9x^2 + 13x - 6), the degree is 3.

Adding and Subtracting Polynomials

Like Terms

• Like Terms: Terms with the same variables raised to the same powers.
• Only like terms can be added or subtracted.
• Example of like terms: (3x^2) and (-2x^2).

Procedure

1. Identify Like Terms: Match terms with the same variables and exponents.
2. Add/Subtract Coefficients: Only coefficients are added/subtracted, keeping the variable part intact.

Methods

Vertical Method

• Align like terms vertically and add/subtract coefficients.

Horizontal Method

• Group like terms together and add/subtract coefficients.

Subtracting Polynomials

• Use distributive property: Distribute the negative sign through the polynomial being subtracted.
• Example:
  • Problem: Subtract ((3x^3 + 8x^2 - 5x + 6)) from ((10x^3 - 5x^2 + 7x - 2)).
  • Distribute negative: (-3x^3 - 8x^2 + 5x - 6).
  • Perform addition/subtraction vertically:
    • (10x^3 - 3x^3 = 7x^3)
    • (-5x^2 + 8x^2 = 3x^2)
    • (7x + 5x = 12x)
    • (-2 - 6 = -8)

Practice and Resources

• Practice problems available in MyMathLab.
• Additional videos on MyMathLab and instructor's YouTube channel.

Conclusion

• Understanding polynomials, their types, and operations are foundational in algebra.
• Ensure mastery of identifying like terms and applying operations correctly.
• Watch recommended videos for further learning and attend team meetings for questions.