Algebraic Expressions Flashcards

Algebraic Expressions

• Composed of constants (numbers) and variables (letter notations).
• Essential for forming equations and functions in mathematics.

Constants

• Defined as numerical values that do not change.
• Fundamental components in algebraic expressions.

Variables

• Represented by letters and can take on different values.
• Used to express general formulas and equations.

Simplification

• Process of combining numbers and like terms in an expression.
• Aims to make expressions easier to work with or understand.

Evaluating the Expression

• Involves simplifying the expression to result in a numerical value.
• Critical step in solving equations.

Order of Operations

• Follow the acronym EMDAS to simplify expressions:
  • E (Exponentiation)
  • M (Multiplication)
  • D (Division)
  • A (Addition)
  • S (Subtraction)

Polynomial Expressions

• Made up of different powers of variables multiplied by constants.
• Terms are connected by addition or subtraction operators.

Terms

• Individual parts of a polynomial that are separated by "+" or "-" signs.
• Each term can contain coefficients and variables.

Coefficient of the Term

• Refers to the numerical factor in front of a variable in a term.
• Helps determine the weight or importance of a term in polynomials.

Degree of a Term

• Calculated by summing the powers of all variables present in that term.
• Indicates the complexity and classification of polynomial terms.

Rule #1 for Terms

• The degree of any non-zero constant term is defined as zero.
• Example: The term "7" has a degree of zero.

Rule #2 for Terms

• The degree of the constant term "0" is not defined.
• Important to acknowledge in polynomial equations.

Degree of the Polynomial

• Represents the highest degree of any term within the polynomial.
• Crucial for understanding the polynomial's behavior and graphing.