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Adding and Subtracting Polynomials

This educational resource provides an in-depth exploration of polynomials, focusing on their definitions, characteristics, and how to perform operations such as addition and subtraction. Understand the terminology including "mono," "bi," "tri," and "poly," and get familiar with the concepts of terms and degrees. Through clear examples and guided practice problems, you'll learn to combine like terms and perform polynomial operations effectively. Enhance your skills with worksheets designed for both classwork and homework, complete with bonus problems for extra practice.

brielle-mendoza
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Adding and Subtracting Polynomials

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  1. Adding and Subtracting Polynomials Tuesday, February 18, 2014

  2. Mono- is a prefix meaning “one” • Bi- is a prefix meaning “two” • Tri- is a prefix meaning “three” • Poly- is a prefix meaning “many” • -nomial is a suffix meaning “terms” • Polynomial = Many Terms What are Polynomials?

  3. We can perform operations with polynomials (addition, subtraction, multiplication, and division). • When we write polynomials, the standard is to write in descending order of the exponents. • The degree of a polynomial is the highest exponent or sum of the exponents if there are multiple variables. How do we work with Polynomials?

  4. Match the polynomial and its degree… • 1. 5p2 – 3 • 2. a3 – 2a2 • 3. 3 – 6n5 – 8n4 • 4. -10x4y3 + 6y3 + 4x4y4 • A. trinomial degree 8 • B. binomial degree 2 • C. trinomial degree 5 • D. binomial degree 3

  5. Adding Polynomials is really… Combining Like Terms

  6. Subtracting Polynomials is really… Adding the Opposite.

  7. Examples: Adding Polynomials (#1) Subtracting Polynomials #(2) (a3 – 2a2) – (3a2 – 4a3) Add the opposite, so… (a3 – 2a2) + (-3a2 + 4a3) Combine like terms… a3 + 4a3 = 5a3 -2a2 + -3a2 = -5a2 5a3 – 5a2 • (5p2 -3) + (2p2 – 3p3) • Identify like terms and combine them. 5p2 + 2p2= 7p2 • Write in descending order of the exponents. • -3p3 + 7p2 -3

  8. Note: It can be easier if you put the exponents in order first. (#16) • (-7x5 + 14 – 2x) + (10x4 + 7x + 5x5) • Reorder • -7x5 + 5x5 +10x4 – 2x + 7x + 14 • Combine like terms • -2x5 + 10x4 + 5x + 14

  9. Remember, when subtracting, add the opposite, then reorder. (#12) • (8n – 3n4 + 10n2) – (3n2 + 11n4 – 7) • 8n – 3n4 + 10n2 + -3n2 + -11n4 + 7 • -3n4 + -11n4 + 10n2 + -3n2 + 8n + 7 • Combine like terms • -14n4 + 7n2 + 8n + 7

  10. Practice makes perfect • Classwork – • Adding and Subtracting Polynomials worksheet (1-30)

  11. Practice some more… • Homework – • Adding and Subtracting Polynomials worksheet (1-20) • # 13 and #17-20 are Bonus Problems – Your Exit Ticket is to circle those problems. Please attempt at least one of them.

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