Math Example--Polynomial Concepts--Adding and Subtracting Polynomials: Example 14

Topic

Polynomials

Description

Subtract the polynomials 5x³ + 9x² + 3x + 9 and 7x³ - 6x² + 5x - 8. Describe the difference of the polynomials. Combine like terms and simplify: (5x³ - 7x³) + (9x² + 6x²) + (3x - 5x) + (9 + 8) = -2x³ + 15x² - 2x + 17. The result is a cubic polynomial with four terms.

The topic of Polynomials is central to algebra. Adding and subtracting polynomials allows students to practice combining like terms and understanding the structure of polynomial expressions. These examples demonstrate the systematic approach to organizing and combining terms.

Seeing multiple worked-out examples is crucial for students to develop a strong understanding of a concept. It allows them to recognize patterns, see commonalities, and build their problem-solving skills.

Teacher’s Script: Let's look at this example together. Notice how we identify and combine like terms. For example, when adding 2x and 5x, we first ensure they are like terms (both have the same variable and exponent). Then, we simply add their coefficients, resulting in 7x. In this case two cubic polynomials are combined to get this cubic polynomial: -2x³ + 15x² - 2x + 17.

For a complete collection of math examples related to Polynomials click on this link: Math Examples: Adding and Subtracting Polynomials Collection.