Post on 03-Jan-2016
description
Warm-Up
Determine the Factored Form of the following polynomial.
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.
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Use your calculator to evaluate the following:
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Synthetic Substitution
When polynomial p(x) is by (x-c) the remainder r will be f(c)
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
Factor Theorem
Factoring Sum/Product Rule
Factor the following quadratics:
A) Roots: -2,-10
B) Roots: -7,5
Sum/Product Rule
Determine the standard form of the quadratic given the roots below:
Roots: 5,6
Roots:-3,5
Roots: -2,-1
Sum/Product Rule
General Setup of the Sum and Product RuleExampleRoots: 71, 3Root 1 Root 2 Final
Sum: 71 3 74
Product:
71 3 213
𝑥2−74 𝑥+213
Quadratic with Imaginary Roots
𝑓 (𝑥 )=𝑥2+2 𝑥+4
𝑥=−2±√22−4 (1)(4)
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𝑥=−2±√−122
𝑥=−1+√3𝑖 𝑥=−1−√3 𝑖ROOTS
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!
You try…
Write the following quadratics in their factored form. Check your answers!
a) b) c)
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