Multiplying Binomials with FOIL
9-12
2
Working with Polynomials
Lesson Details
Grade Level
9-12
Duration (minutes)
3
Summary
A Grade 9-12 math lesson covering three polynomial skills — identifying terms, coefficients, constants, and degree; writing a polynomial in standard form from highest to lowest degree; and adding polynomials by combining like terms — each demonstrated with a fully worked example.
Student Worksheet: Working with Polynomials
Teacher Note: Students can watch the video lesson above and answer the questions. Click the “Teacher Answer Key” dropdown below when you are ready to review the solutions!
Key Concepts:
• Parts of a Polynomial: Terms are separated by + or − signs (the sign stays attached to its term); a coefficient is the number multiplying the variable; a constant has no variable.
• Degree: The degree of a polynomial is its highest exponent — you don’t add exponents together, just find the largest one.
• Standard Form: Write the terms of a polynomial from highest degree to lowest degree. Only the order changes; the values stay the same.
• Like Terms: Like terms have the same variable and the same exponent. Combine them by adding or subtracting their coefficients.
Instructions: Read each question carefully and write your answer in the space provided.
- Question 1: List the terms of 4x³ + 2x² − 5x + 7. Why is the third term written as −5x and not 5x?
- Question 2: Identify the coefficient of each term in 4x³ + 2x² − 5x + 7, and identify the constant term.
- Question 3: What is the degree of 4x³ + 2x² − 5x + 7? How do you find it?
- Question 4: Rewrite 5x − 3 + 2x² in standard form. Show the degree of each term first.
- Question 5: Add 3x² + 4x + x² − 2x by grouping and combining like terms. Show your steps.
Click to reveal Teacher Answer Key
1. The terms are 4x³, 2x², −5x, and 7. The negative sign stays attached to its term.
2. Coefficients: 4, 2, and −5. Constant: 7.
3. The degree is 3. It’s the highest exponent in the polynomial, not the sum of all the exponents.
4. 2x² is degree 2, 5x is degree 1, −3 is degree 0. Standard form: 2x² + 5x − 3.
5. Group: (3x² + x²) + (4x − 2x). Combine: 3x² + x² = 4x², and 4x − 2x = 2x. Result: 4x² + 2x.
Disclaimer: This worksheet was generated with AI assistance based on original video content. It is intended for educational reference only. Teachers are encouraged to review and adjust questions to fit their curriculum standards before classroom use.
🎯 Extension Activity: Given the polynomial 6x − 4 + 3x², identify its degree and rewrite it in standard form. Then add 5x² + 3x + 2x² − x by combining like terms. Show every step for both.