Complete the Theorem chart.
|Rational Zero Theorem||________________________________________________________________|
What form does the divisor need to be in to use synthetic division? ____________________
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
p(x). Call this n.
- Then the number of ____________ of
p(x)is less than or equal to n.
- Further, the possible number of ____________ is ____________
- To find the number of ____________ of
p(x), write p(−x)in descending order as above (i.e. change the sign of all terms in p(x)with odd powers), and repeat the process above. Then the ____________ number of negative roots is n.
Here are the steps (via example) to synthetic division:
Use synthetic division to divide the following polynomials. Write out the remaining polynomial.
Find all real zeros of the following polynomials, given one or two 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
x3−5x2−2x+10by using synthetic division to find the x−intercepts and locate the y−intercepts.
Write a 5th degree equation of a polynomial function with the zeroes: 0 (multiplicity 2), 2 (multiplicity 3), and -5 (multiplicity 2)