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Adding and Subtracting Polynomials

Adding and Subtracting Polynomials. Section 10.1. Polynomial. Section 10.1. -- An expression with several terms that are added or subtracted together, such as: 5x 4 + 3x 3 – 10x 2 + 17x – 9 10x 5 – 9x 4 + 13x 3 + 23x 2 – ½ x + 7

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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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