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Subtracting Polynomials Practice Worksheet
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Subtracting Polynomials Practice Worksheet
📚 Part 1: Basic Polynomial Subtraction
Directions: Subtract the polynomials. Show your work by distributing the negative sign and combining like terms.
1. (3x² + 5x - 2) - (x² + 3x + 1)
2. (7y³ - 4y² + 6y) - (2y³ + y² - 3y + 5)
3. (4a² - 7a + 9) - (-2a² + 5a - 3)
4. (6m³ + 2m - 8) - (3m³ - 4m² + m + 1)
🎯 Part 2: Multiple Choice
Directions: Choose the correct answer for each subtraction problem.
5. What is (5x² + 3x - 1) - (2x² - x + 4)?
3x² + 4x - 5
3x² + 2x - 5
7x² + 2x + 3
3x² + 4x + 3
6. Simplify: (8y² - 3y + 7) - (4y² + 2y - 1)
4y² - 5y + 8
4y² - y + 6
12y² - y + 6
4y² + y + 8
7. What is (10z³ - 6z + 2) - (3z³ + 4z² - 2z - 5)?
7z³ - 4z² - 4z + 7
7z³ + 4z² - 8z - 3
13z³ + 4z² - 8z - 3
7z³ - 4z² - 8z - 3
✏️ Part 3: Word Problems and Application
8. The area of rectangle A is represented by the polynomial (6x² + 4x + 8). The area of rectangle B is represented by (2x² - x + 3). Write a polynomial expression for how much larger rectangle A is than rectangle B.
9. A company's profit for the first quarter can be modeled by P₁ = 4x³ + 7x² - 5x + 12, and their costs by C₁ = x³ + 3x² + 2x - 4. Write and simplify an expression for their net earnings (profit minus costs).
10. Challenge Problem: Subtract (3a²b - 5ab² + 7ab) - (a²b + 2ab² - 3ab + 4)
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