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Adding and Subtracting Polynomials

Learn to classify polynomials by terms and degrees, identify leading coefficients, and combine like terms in this comprehensive guide. Practice adding and subtracting polynomials with examples and exercises. Discover the standard form of polynomials for efficient calculation.

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Adding and Subtracting Polynomials

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  1. Adding and Subtracting Polynomials Section 10.1

  2. Polynomial • Section 10.1 -- An expression with several terms that are added or subtracted together, such as: • 5x4 + 3x3 – 10x2 + 17x – 9 • 10x5 – 9x4 + 13x3 + 23x2 – ½ x + 7 • If the x-terms have different exponents, they cannot be added together.

  3. Classifying polynomials – by the number of terms • Monomial-polynomial with 1 term • Binomial-polynomial with 2 terms • Trinomial-polynomial with 3 terms

  4. Polynomials can also be classified by Degree. The degree of a polynomial is determined by the term with the largest exponent: 7x4 + 3x3 – 10x2 + 17x – 9 is a 4th degree polynomial. 7 is the LEADING COEFFICIENT. 10x5 – 9x4 + 13x3 + 23x2 – ½ x + 7 is a 5th degree polynomial. 10 is the LEADING COEFFICIENT. • Leading coefficients are the number in front of the term with the highest exponent

  5. Can also classify polynomials by the highest exponent. • 0 degree-constant • 1st degree-linear • 2nd degree-quadratic • 3rd degree- cubic • 4th degree-quartic

  6. More about Polynomials • All exponents must be whole numbers • f(x) = 5x3 + 2x-1 These are not polynomials • f(x) = 4x2 + 3x Standard form of a Polynomial – arrange the terms left to right starting with the highest exponent: 7x5 + 10x4 – 12x3 + 17x2 – 9x + 6 10x5 + 7x3 – 2x + 1 • .

  7. Adding or Subtracting Poly’s • Add (or subtract) like terms—x3 and x3 etc.

  8. Example • (2x2 + 4x + 1) + (x3 – 6x2 + 4)

  9. Adding and Subtracting Polynomials Combine like terms with the same exponents (10x5 – 9x4 + 13x3 + 23x2 – 4x + 7) + (5x4 + 3x3 – 10x2 + 17x – 9)

  10. (7x3 + 2x2 – 9x + 3) + (4x2 + 12x + 9) Another way to add or subtract – use the Vertical or Column Format

  11. Homework • page 580; 20-46 even

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