Warm-Up

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Warm-Up

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1. Warm-Up • Determine the Factored Form of the following polynomial.

2. Synthetic Substitution and Imaginary Roots

3. Learning Targets • Use synthetic substitution to evaluate our polynomial at different inputs • Look at imaginary roots and determine how to write them in factored form • Learn the Sum-Product Rule to check our work and sure that our roots are correct.

4. Decide whether a root exists at the given value: state your reason. 1 • 2 • 3 • 4

5. Use your calculator to evaluate the following: 1 • 2 • 3 • 4

6. Synthetic Substitution • When polynomial p(x) is by (x-c) the remainder r will be f(c)

7. Factor Theorem When f(c)=0 then x-c is a factor of the polynomial. AND When x-c is a factor of the polynomial then f(c)=0

8. Factoring Sum/Product Rule • Factor the following quadratics: A) Roots: -2,-10 B) Roots: -7,5

9. Sum/Product Rule • Determine the standard form of the quadraticgiven the roots below: • Roots: 5,6 • Roots:-3,5 • Roots: -2,-1

10. Sum/Product Rule General Setup of the Sum and Product Rule Example Roots: 71, 3

11. Imaginary Roots • However we should always evaluate these pairs of roots to see if we are left with our original quadratic. Simplify and Distribute This is the quad we started with!

12. You try… • Write the following quadratics in their factored form. Check your answers! a) b) c)

13. Activity: Polynomial Puzzle • Pick a card • Using that card’s instructions you have to fill out the four section paper • You will be designing your own polynomial • Don’t make it impossible and don’t make it too easy – use your best judgment!!! • After filling out the four section paper cut out each square and mark it using a symbol followed by what period you attend • Keep the four pieces together and turn them in

14. For Tonight: • Worksheet