Vocabulary
Complete the Theorem chart.
Name  Theorem 
Remainder Theorem  ________________________________________________________________ 
Factor Theorem  ________________________________________________________________ 
Rational Zero Theorem  ________________________________________________________________ 
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What form does the divisor need to be in to use synthetic division? ____________________
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Fill in the blanks about Descartes Rule of Signs:
Given any polynomial, ,
 Write it with the terms in ____________ order, i.e. from the ____________ degree term to the ____________ degree term.
 Count the number of ____________ of the terms in . Call this .
 Then the number of ____________ of is less than or equal to .
 Further, the possible number of ____________ is ____________
 To find the number of ____________ of , write in descending order as above (i.e. change the sign of all terms in with odd powers), and repeat the process above. Then the ____________ number of negative roots is .
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Synthetic Division
Here are the steps (via example) to synthetic division:
Divide by .
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Use synthetic division to divide the following polynomials. Write out the remaining polynomial.
 Find if
Find all real zeros of the following polynomials, given one or two zeros.
Real Zeros

Use the rational zero theorem and synthetic division to find all the possible rational zeros of the polynomial

Use Descartes Rule of Signs to identify the possible number of positive and negative roots of

Find the root(s) of

Graph the polynomial function by using synthetic division to find the intercepts and locate the intercepts.

Write a 5th degree equation of a polynomial function with the zeroes: 0 (multiplicity 2), 2 (multiplicity 3), and 5 (multiplicity 2)