Polynomial operations involve adding, subtracting, and multiplying expressions containing variables and coefficients. When adding or subtracting, combine like terms (terms with the same variable and exponent). When multiplying, use the distributive property to multiply each term in one polynomial by each term in the other. Remember the rules for exponents: when multiplying terms with the same base, add the exponents.
Match each term with its definition:
| Term | Definition |
|---|---|
| 1. Polynomial | A. A single number or variable, or numbers and variables multiplied together. |
| 2. Coefficient | B. A term that has no variable factor. |
| 3. Term | C. An expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents. |
| 4. Like Terms | D. The numerical factor of a term. |
| 5. Constant | E. Terms that have the same variable(s) raised to the same power(s). |
Answers: 1-C, 2-D, 3-A, 4-E, 5-B
Fill in the blanks with the correct terms to complete the statements about polynomial operations.
When adding or subtracting polynomials, you can only combine _____ _____. To multiply a polynomial by another polynomial, use the ______ property to multiply each term in the first polynomial by each term in the second polynomial. The ______ of a term is the numerical factor of the term.
Word Bank: Like Terms, Distributive, Coefficient
Answers: Like Terms, Distributive, Coefficient
Explain in your own words why it's important to only combine "like terms" when adding or subtracting polynomials. Provide an example to support your explanation.
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