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Understanding Polynomial Operations: Addition, Subtraction, and Multiplication Techniques

This chapter focuses on the objectives of adding, subtracting, and multiplying polynomials. Key vocabulary includes monomials, binomials, and trinomials, essential for understanding polynomial structure. Readers will learn to identify degrees of polynomials and simplify expressions using techniques like the FOIL method for multiplying binomials. Examples illustrate how to simplify various polynomial expressions, providing clear and concise methods for performing operations. This foundational knowledge is crucial for mastering polynomial manipulation in algebra.

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Understanding Polynomial Operations: Addition, Subtraction, and Multiplication Techniques

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  1. Chapter 5 Section 5.2

  2. Objectives • To add, subtract, and multiply polynomials.

  3. Vocabulary _____ ______ are two monomials that are the same, or differ only by their numerical coefficients. A _______________ is a monomial or a sum of monomials. Trinomial  Binomial  The _________ of a polynomial is the _______of the monomials with the greatest __________. Like Terms polynomial Tri = 3; Nomial = Number Bi = 2; Nomial = Number degree degree degree

  4. Example State the degree of the polynomial. x4y3– 21x3 Answer: 7

  5. Example Simplify (4x2- 3x) – (x2 + 2x – 1) Answer: 3x2 – 5x + 1 (4x2- 3x) + (x2 + 2x – 1) Answer: 5x2 –x - 1

  6. Example (4n + 3)(3n + 1) FOIL!

  7. FOIL • F – the product of the first terms • O – the product of the outer terms • I – the product of the inner terms • L – the product of the last terms.

  8. Example (4n + 3)(3n + 1) Answer: 12n2+ 13n + 3

  9. Example (k2 + 3k + 9)(k+3) Answer: k3 + 6k2 + 18k + 27

  10. Simplify 11x + y • (5x – 7y) + (6x + 8y) • 3y(2x+6) • (x+6)(x+3) • 2m2n(5mn – 3m3n2 + 4mn4) • (2p – 3s)2 6xy + 18y x2 + 9x + 18 10m3n2 – 6m5n3 + 8m3n5 4p2 – 12ps+ 9s2

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