Algebra 1 - Module 1 Lesson 1 Vocabulary

Study Notes

Algebraic Expression: Can be a numerical symbol, variable symbol, or the result of placing algebraic expressions into operators (addition, subtraction, multiplication, division) or exponentiation with rational exponents.
Constant Term of a Polynomial: Achieved by substituting 0 for variable symbols in a polynomial, yielding 'a sub zero'.
Degree of a Monomial: Calculated by summing the exponents of variable symbols in a nonzero monomial.
Degree of a Polynomial: Determined by identifying the highest degree among the terms within the polynomial.

Equivalent Algebraic Expressions: Two expressions are equivalent if one can be transformed into the other using commutative, associative, distributive properties, and rational exponent properties.
Equivalent Numerical Expressions: Two numerical expressions are equivalent if they produce the same numerical result.

Graph of an Equation in Two Variables: Represents all points in the coordinate plane that satisfy the equation.
Piecewise Linear Function: Defined over finite non-overlapping intervals with different linear functions applying to each interval.

Leading Term and Leading Coefficient: The leading term is the first term of a polynomial in standard form, and the leading coefficient is the numerical factor in front of this term.
Monomial: A type of polynomial expression formed exclusively through multiplication. Consists of products of numerical or variable symbols.
Polynomial Expression: Can consist of a numerical expression, variable symbol, or the result of adding/multiplying two polynomial expressions.

Solution: A number that makes an equation true when substituted for the variable.
Solution Set: The collection of all solutions to an equation.
Variable Symbol: Represents a placeholder for a number; its constraints may vary by context (e.g., integers or positive real numbers).
Zero Product Property: States that if the product of two numbers equals zero, at least one of those numbers must also be zero.