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Warm Up

Warm Up. Foil (3x+7)(x-1). Factors, Roots and Zeros. Definition: Factoring. Terms are Factors if , when they are multiplied, they equal that poly. Example. Answer: (x-3)(x+5). ( x - 3) and ( x + 5) are Factors of the polynomial. Definition: Solutions or Roots.

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Warm Up

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  1. Warm Up Foil (3x+7)(x-1)

  2. Factors, Roots and Zeros

  3. Definition: Factoring Terms are Factorsif, when they are multiplied, they equal that poly

  4. Example Answer: (x-3)(x+5) • (x - 3) and (x + 5) are Factors of the polynomial

  5. Definition: Solutions or Roots • The solutions to a poly are the points where the graph crosses the x-axis. • Also called Roots or x-intercepts. • All the same thing! • Solutions = Roots = x-intercepts • Picture…

  6. Graph of a Polynomial Function Here is the graph of our polynomial function: The Zeros of the Polynomial are the values of x when the polynomial equals zero. In other words, the Zeros are the x-values where y equals zero.

  7. Identifying Solutions Example f(x) = x2 - 4 Solutions are -2 and 2.

  8. Identifying Solutions Now you try this problem. f(x) = 2x - x2 Solutions are 0 and 2.

  9. x y -2 -1 1 3 4 Graphing Quadratic Equations Try this problem y = x2 - 2x - 8. Roots? Zeros?

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