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6.1 Polynomial Functions

6.1 Polynomial Functions. Monomial – an expression that is either a variable, a real number or the product of a real number and variables with whole number exponents. Polynomial – a monomial or the sum of monomials Degree – the sum of the exponents of a term

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6.1 Polynomial Functions

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  1. 6.1 Polynomial Functions

  2. Monomial – an expression that is either a variable, a real number or the product of a real number and variables with whole number exponents.

  3. Polynomial – a monomial or the sum of monomials • Degree – the sum of the exponents of a term • Always put answers in standard form – descending order of exponents

  4. By Degree 0 – constant 1 – linear 2 – quadratic 3 – cubic 4 – quartic 5 - quintic By # of Terms 1 – monomial 2 – binomial 3 – trinomial 4 or more - polynomial Classifying a Polynomial

  5. EX 1 • Classify: 9 + x3

  6. EX 2 • Classify: x3 – 2x2 – 3x4

  7. EX 3 • Write in standard form and classify: • p(p – 5) + 6

  8. EX 4 • Write in standard form and classify: • (x + 1)(x – 2)(x + 3)(x – 4)

  9. Notes 6.2 Polynomial & Linear Factors

  10. EX 1 • Write in factored form: • 3x3 - 18x2 + 24x

  11. Zeros = Roots = Solutions = X-intercepts

  12. EX 2 • Find the zeros and graph: • y = (x + 1)(x – 1)(x + 3)

  13. EX 3 • Find the zeros and graph: • y = (x – 7)(x – 5)(x – 3)

  14. EX 4 • Write an equation in standard form with zeros at 2, -3, 0.

  15. If a linear factor of a polynomial is repeated then the zero is repeated – multiple zero. • A multiple zero has a multiplicity equal to the number of times the zero occurs.

  16. EX 5 • Find any multiple zeros and state the multiplicity. • f(x) = x5 – 6x4 + 9x3

  17. Equivalent Statements about Polynomials • -4 is a solution of x2 + 3x – 4 = 0 2. -4 is an x-intercept of the graph y = x2 + 3x – 4 • -4 is a zero of y = x2 + 3x – 4 4. x + 4 is a factor of x2 + 3x - 4

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