PRE-CALCULUS 6.0
WS 2.4
More Practice
DesCartes’ Rule and Finding Real of Polynomial Functions
A.
Use Descartes’ Rule with the function shown below to generate a table of all
of the possible distributions of zeros between + Real, - Real, and Complex
numbers. (Note: Do not solve – just generate the cases)
f ( x) = 7 x7 + 6 x6 − 5 x5 + 4 x4 + 3 x3 − 2 x2 + x + 1
Case
B.
+ Real
- Real
Complex
Total
Find all of the zeros of the following functions and write out the function in
fully factored form. Remember that if the fully factored form is expanded
(i.e. multiplied out), it must produce the original polynomial.
Keep in mind the following tools to help you accomplish this task:
1)
2)
3)
4)
5)
6)
7)
8)
GCF Factoring
Quick Check for ±1 as zeros
Descartes’ Rule of Signs and Fundamental Theorem of Algebra
Rational Zero Test (list of p/q)
Synthetic Division, Factor/Remainder Theorems
Intermediate Value Theorem
Upper and Lower Bound Rules
Quadratic Solution Methods
a. f ( x ) =
x 5 + 5 x 4 + 10 x 3 + 10 x 2 + 5 x + 1
b. f ( x ) = x 5 + 5 x 4 + 3 x 3 − 13 x 2 − 8 x + 12
c. f ( x ) = x 5 + x 4 − 16 x 3 − 4 x 2 + 48 x
d. f ( x ) = 4 x 7 + 4 x 6 − 23 x 5 − 18 x 4 + 33 x 3 + 18 x 2