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Understanding Polynomials: Definitions, Degrees, and Simplification Techniques

This guide covers the fundamental vocabulary related to polynomials, including monomials, binomials, and trinomials. It explains the concept of like terms, where terms share the same variable and exponent, as well as how to find the degree of a polynomial by identifying the highest degree of its monomials. Step-by-step examples illustrate how to determine if an expression is a polynomial, find its degree, and simplify polynomial expressions. Key examples include combining and simplifying terms for clarity and comprehension.

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Understanding Polynomials: Definitions, Degrees, and Simplification Techniques

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  1. 5.2Polynomials

  2. Vocabulary polynomial: a monomial or the sum of monomials binomial: 2 terms trinomial : 3 terms Like terms: same variable and same exponent Note: terms are separated by + or –

  3. Degree monomial The sum of the exponents of the variables x2y3z polynomial Find the degree of each term (monomial), then take the highest degree x2 + 4vgz

  4. Ex 1 Determine if the following is a polynomial, and its degree if it is. Example 2-1a

  5. Ex 2 Determine if the following is a polynomial, and its degree if it is. Example 2-1a

  6. Ex 3 Simplify Example 2-1a

  7. Ex 4 Simplify Example 2-1a

  8. Ex 5 Simplify Example 2-1a

  9. Ex 6 Simplify Example 2-1a

  10. Ex 7 Simplify Example 2-1a

  11. Ex 8 (a2 + 3a – 4)(a + 2)

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