WarmUp Synthetic Substitution and Imaginary Roots Learning Targets

Warm-Up �

Synthetic Substitution and Imaginary Roots

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.

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

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

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

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

Factoring Sum/Product Rule �

Sum/Product Rule �

Sum/Product Rule � Root 1 Root 2 Final Sum: 71 3 74 Product: 71 3 213

Quadratic with Imaginary Roots ROOTS

Imaginary Roots � Simplify and Distribute This is the quad we started with!

You try… �

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

For Tonight: �Worksheet