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Warm-Up: p. 429 #30, 32

Warm-Up: p. 429 #30, 32. 30) Evaluate x 4 +2x 3 +2 for x=-2 32) Evaluate -4x 3 +1+x for x=3. Homework due today. Section 7.1. Polynomials. Essential Questions. How do we name, identify, add , and subtract polynomials. Monomial.

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Warm-Up: p. 429 #30, 32

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  1. Warm-Up: p. 429 #30, 32 • 30) Evaluate x4+2x3+2 for x=-2 • 32) Evaluate -4x3+1+x for x=3

  2. Homework due today

  3. Section 7.1 Polynomials

  4. Essential Questions • How do we name, identify, add, and subtract polynomials.

  5. Monomial • A number, a variable, or a product of a number and one or more variables. • Examples: • 3x • -5x2 • ½ • -73x3y2

  6. Constant • A monomial with no variables. • Just a number • Examples: • 3 • ½ • -2.4

  7. Coefficient • The number part of a monomial • Not exponents • Examples: • x3 has a coefficient of 1 • -4t2 has a coefficient of -4 • -ab has a coefficient of -1 • has a coefficient of -2/3

  8. Degree of a Monomial • The sum of the exponents of its variables. • Examples: • 4xy2 has degree 1+2=3 • -3x2yz2 has degree 2+1+2=5 • Any constant has degree 0

  9. You-Try: Identify the coefficient and degree • -3x2y • x13 • -2x2y2z

  10. Names based on Degree

  11. Warm-Up: November 6, 2012 • Identify the coefficient and degree of the following monomials:

  12. Continuing the 7.1 notes from yesterday.

  13. Standard Form • Combine like terms • Write terms in descending order of degree. • Exponents go from largest to smallest • 7x-5+3x2-2x  3x2+5x-5 • -2x3+3x4+2x3+5  3x4+5

  14. Polynomials – In Standard Form • Monomial: One term • Binomial: Two terms; the sum of two monomials • Trinomial: Three terms; the sum of three monomials • Polynomial: One or more terms; the sum of one or more monomials

  15. Example 1 • Classify each polynomial by degree and number of terms • 1) x2+4-8x-2x3 • Cubic Polynomial • 2) 3x3+2-x3-6x5 • Quintic Trinomial

  16. What is not a polynomial • If any x has a negative exponent (or is in the denominator) • If any x has a fraction or decimal exponent • If any x is inside a square root • If any x is an exponent

  17. Adding and Subtracting Polynomials • Combine like terms • Write answer in standard form

  18. Example - Addition • (2x4+4x3+5x-2)+(-2x4-7x2+8x-10)

  19. Example - Subtraction • (3x3-12x2-5x+1)-(-x2+5x+8)

  20. Assignment • Page 429-430 #29, 31, 39-49 odd

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