Symbolic Mathematical Formulas Quiz

Symbolic Mathematical Formula: Key Points

• An algebraic expression is made up of variables, constant algebraic numbers, and algebraic operations such as addition, subtraction, multiplication, division, and exponentiation.
• Transcendental numbers like π and e are not algebraic since they are not derived from integer constants and algebraic operations.
• A rational expression is an expression that can be rewritten as a rational fraction using the arithmetic operations.
• A rational equation is an equation where two rational fractions are set equal to each other.
• Algebra has its own terminology to describe parts of an expression, such as coefficients, variables, and exponents.
• The roots of a polynomial expression of degree n can always be written as algebraic expressions if n < 5.
• Letters at the beginning of the alphabet are typically used to represent constants, while those toward the end of the alphabet are used to represent variables.
• Terms with the highest power (exponent) are written on the left, and coefficients of one are usually omitted.
• A rational algebraic expression is a quotient of polynomials, while an irrational algebraic expression is not rational.
• The table summarizes how algebraic expressions compare with other types of mathematical expressions.
• Algebraic solutions do not exist for all polynomial equations if n ≥ 5, according to the Abel-Ruffini theorem.
• Division by zero is undefined, so a solution causing formal division by zero is rejected in rational equations.