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Algebra I Recipe: Adding and Subtracting Polynomials
A. Definitions
  1. polynomial – has one or more terms
  2. monomial – has one term
  3. binomial – has two terms
  4. trinomial – has three terms
  5. degree of ONE term – it’s the sum of all exponents in the term.
  6. degree of a POLYNOMIAL:
    • Find the degree of each term.
    • The largest degree is the degree of the polynomial.
  7. standard form of a polynomial – terms written in order from largest degree to smallest degree.
B. Adding Polynomials
  1. Change all subtraction to adding the opposite.
  2. Drop the parentheses.
  3. Combine like terms.
  4. State the answer in standard form.
ExamplesExamples:
(-4x2 - 2x + 5) + (6x2 + 2x – 11)

(9x3 + 3x2 - 24) + (-9x2 + 5x + 19)

C. Subtracting Polynomials
  1. Change all subtraction to adding the opposite when necessary.
  2. The negative in front of the second set of parentheses is understood to be a –1.
  3. To eliminate the parentheses, distribute the –1. Remember that distributing by -1 will change each term to its opposite.
  4. Combine like terms.
  5. State the answer in standard form.
ExamplesExamples:
(8x3 - 3x2 - 11x – 3) – (-13x3 - 3x2 + 2x – 17)

(9x3 - 3x2 - 1) – (9x3 + 5x2 + 19)




G Redden

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