Adding and Subtracting Polynomials
Description: This lesson will teach you how to add and subtract polynomials. We will go through six examples, practice exercises, and provide solutions. By the end of the lesson, you should be able to perform these operations confidently.
Lesson Outline:
- What is a Polynomial?
- Adding Polynomials
- Subtracting Polynomials
- Examples
- Exercises
- Homework
- Revision
1. What is a Polynomial?
A polynomial is an algebraic expression made up of terms, where each term includes a variable raised to a non-negative integer power and has a coefficient. For example, \( 3x^2 + 2x - 5 \) is a polynomial.
2. Adding Polynomials
To add polynomials, combine like terms, which are terms with the same variable raised to the same power. For example:
Example 1: Add \( (3x^2 + 2x + 1) + (2x^2 - 3x + 4) \)
Solution:
3. Subtracting Polynomials
To subtract polynomials, subtract each term in the second polynomial from the corresponding term in the first polynomial. For example:
Example 2: Subtract \( (2x^2 + 4x - 7) - (x^2 - 3x + 2) \)
Solution:
4. Examples
Example 3: Add \( (5x^3 - 2x + 3) + (2x^3 + 4x - 6) \)
Example 4: Subtract \( (4x^2 - 6x + 2) - (x^2 + 3x - 5) \)
5. Exercises
Exercise 1: Add \( (3x^2 + x + 4) + (x^2 - 2x + 6) \)
Solution: \( 4x^2 - x + 10 \)
Exercise 2: Subtract \( (7x^3 + 2x - 5) - (2x^3 - x + 3) \)
Solution: \( 5x^3 + 3x - 8 \)
6. Homework
Solve the following problems:
- Add: \( (4x^2 - 3x + 2) + (x^2 + 5x - 7) \)
- Subtract: \( (6x^3 + 2x - 4) - (2x^3 - 4x + 3) \)
7. Revision
Review the key concepts of adding and subtracting polynomials. Make sure you understand how to combine like terms and simplify your expressions.
YouTube Video Explanation
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