Operations of Polynomials Math Activities

Definition

Operations of polynomials refer to the basic arithmetic processes—addition, subtraction, multiplication, and division—performed on polynomial expressions. A polynomial is an algebraic expression made up of terms consisting of variables raised to whole-number exponents and coefficients.

Summary

1. Addition and Subtraction

• Combine like terms (terms with the same variables and exponents).
• Rearranged as:

• Subtract by distributing the negative sign before combining:

2. Multiplication

• Distributive Property: Multiply each term in one polynomial by each term in the other.
• Use FOIL for binomial × binomial:

• For larger polynomials:
  Use vertical or horizontal multiplication formats to organize terms before combining like terms.

3. Division

• Monomial Divided by Monomial: Divide coefficients and subtract exponents:

• Polynomial Division:
  • Long Division: Similar to numerical long division.
  • Synthetic Division: Shortcut used when dividing by linear expressions like x−c.

4. Special Products

• Square of a binomial:

• Difference of squares:

5. Applications

• Used in algebraic simplification, equation solving, area problems, and function operations.
• Foundation for more advanced topics such as factoring, graphing polynomials, and calculus.

Operations of Polynomials Math Activities

This is a fantastic bundle which includes 10 activities with answer guides about Operations of Polynomials. All our worksheets are completely editable so can be tailored for your curriculum and target audience.

Resource Examples

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Worksheets Activities Included

•  Combine Like Terms (Addition)
• Subtract Polynomials Carefully
• Distribute a Monomial
• Multiply Two Binomials (FOIL)
• Binomial × Trinomial
• Special Products
• Multiply and Then Combine
• Polynomial Long Division (Non-zero Remainder)
• Synthetic Division & Remainder Theorem
• Mixed Operations & Classification