polynomials and algebraic expressions worksheet - Free Printable

Let’s solve this step by step.

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Part A: Matching Type

We match each definition in Column A with the correct term in Column B.

1. A term with no variables → This is a Constant.
(Example: 5, -3, 0 — these are constants because they don’t have letters like x or y.)

2. Numbers attached to variables in a term → This is a Coefficient.
(Example: In 4x, the number 4 is the coefficient.)

3. A part of an algebraic expression separated by “+” or “-” signs → This is a Term.
(Example: In 3x + 2y – 7, there are three terms: 3x, 2y, and -7.)

4. A polynomial with two terms → This is a Binomial.
(Example: x + 5, or 2a – 3b — both have exactly two terms.)

5. Terms with the same variable(s) of the same degree → These are Like terms.
(Example: 3x² and 5x² are like terms; but 3x² and 3x are not.)

So matches:

1 → Constant
2 → Coefficient
3 → Term
4 → Binomial
5 → Like terms

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Part B: Polynomial or Not?

Remember: A polynomial must have:
- Only non-negative integer exponents (no negative or fractional exponents)
- No variables in denominators
- No variables under square roots (unless it simplifies to whole numbers)

Let’s go one by one:

6. –7x + y → Both terms have variables with exponent 1 (which is fine). ✔ POLYNOMIAL

7. 4x / y → Variable y is in denominator → ✘ NOT POLYNOMIAL

8. 8mn⁻¹ → Negative exponent on n → ✘ NOT POLYNOMIAL

9. 5(x – 3) → Expand: 5x – 15 → all exponents are 1 or 0 → ✔ POLYNOMIAL

10. √(6m²) + 1 → √(6m²) = m√6 → which is same as (√6)m¹ → still a valid term? Wait — actually, √(6m²) simplifies to |m|√6, but since we’re dealing with polynomials over real numbers and assuming m ≥ 0 for simplicity, it becomes a linear term. BUT — strictly speaking, if the original expression has a radical that doesn’t simplify to a rational coefficient times a power, it may not be considered a polynomial. However, √(6m²) = √6 * |m| — absolute value makes it NOT a polynomial unless restricted. But in many school contexts, if it simplifies to a monomial,