A mathematical phrase with operators connecting numbers and variables is an expression. 4. A polynomial is an algebraic expression made by adding or subtracting terms. 7. The exponent of the term with the greatest exponent is the leading exponent. 10. Numbers or variables that form a product are factors. 11. Terms that have the same variable(s) raised to the same exponent(s) are like terms. 12. Terms with different variables, or the same variables raised to different exponents are unlike terms. 13. A letter representing a number or value that can change or vary is a variable. 14. A three-termed polynomial is a trinomial. 15. A term with no variables, that’s value remains the same is a constant term. 16. When the terms of a polynomial are ordered from highest to lowest degree is known as standard form. Down 1. A one-termed polynomial is a monomial. 2. In a term, the sum of the exponents on the variables is the degree. 5. Numbers, variables, and the products of numbers and variables are all terms. 6. The number that a variable is being multiplied with is called the coefficient. 8. An equation is a mathematical statement that says two expressions are equal. 9. A two-termed polynomial is a binomial.
The Correct Answer and Explanation is:
Answer Key:
Across:
3. Expression
4. Polynomial
7. Leading Exponent
10. Factors
11. Like Terms
12. Unlike Terms
13. Variable
14. Trinomial
15. Constant Term
16. Standard Form
Down:
- Monomial
- Degree
- Terms
- Coefficient
- Equation
- Binomial
Explanation
Understanding algebraic vocabulary is essential for mastering mathematical expressions and solving equations. Let’s break down these key terms.
An expression (3 Across) is a mathematical phrase combining numbers, variables, and operators (like +, −, ×). When expressions include variables (symbols representing unknown or changeable values), they can form a polynomial (4 Across)—a sum or difference of terms.
Each part of a polynomial separated by + or − is called a term (5 Down). A monomial (1 Down) has one term, a binomial (9 Down) has two, and a trinomial (14 Across) has three. The degree (2 Down) of a term is the sum of the exponents on its variables; the highest degree term in a polynomial gives its overall degree. The exponent on that highest-degree term is called the leading exponent (7 Across).
The standard form (16 Across) of a polynomial orders its terms from highest to lowest degree. Some terms have no variables; these are constant terms (15 Across) because their value doesn’t change. A coefficient (6 Down) is the number multiplying a variable in a term.
Terms are considered like terms (11 Across) if they have the same variable(s) raised to the same power(s). Otherwise, they are unlike terms (12 Across). Simplifying expressions often involves combining like terms.
Multiplying parts of terms, such as numbers or variables, involves factors (10 Across). Lastly, an equation (8 Down) is a mathematical sentence asserting that two expressions are equal, usually solved to find the value of a variable (13 Across).
These terms form the foundation of algebra and are essential for solving equations, simplifying expressions, and understanding mathematical structure.
