PVC Descartes Rules of Sign to Determine the Posible Number in Algebra Question

24.Use Descartes’ Rule of Signs to determine the possible number of positive and negative
real zeros. Be sure to include all possibilities.
9 ( x )
–
–
–
12×4 – 11×3 + 77×2 – 11x – 5
Answer: Number of Positive Real Zeros:
Number of Negative Real Zeros:
25.
Consider the following polynomial.
G ( x ) = x3 + x2 – 32x – 60
–
–
Step 1. Use Descartes’ Rule of Signs to determine the possible number of positive and
negative real zeros. Be sure to include all possibilities.
Answer: Number of Positive Real Zeros:
Number of Negative Real Zeros:
Step 2. Use synthetic division to identify integer bounds of the real zeros. Find the least
upper bound and the greatest lower bound guaranteed by the Upper and Lower Bounds
of Zeros theorem.
Answer: Upper Bound:
Lower Bound:
www.fsc.org
MIX
9781544355184
Paper from
responsible sources
FSC C011825
SSAGE www.sagepublishing.com
Lege London New Delhi Singapore I Washington DC | Melbourne
Step 3. Using your answers to the previous steps, polynomial division, and the quadratic
formula, if necessary, find all of the zeros of the polynomial. Include multiples of the
same zero where applicable.
Answer:
26.
Consider the following polynomial.
H (x) = x3 – 6×2 – 2x + 12
=
–
Step 1. Use the Rational Zero Theorem to list all of the potential rational zeros.
Answer:
+{
Step 2. Use polynomial division and the quadratic formula, if necessary, to identify the
actual zeros.
Answer:
27.
Find all solutions of the following polynomial equation.
–
–
10×2 – x + x3 – 10 = 0
Answer:
28.
Consider the following polynomial function.
(x
f(x) = (x + 3)2(x – 2) (x – 1)
=
–
–
Step 1. Find the degree and the y-intercept. Express the intercept as an ordered pair.
Degree:
y-intercept:
Step 2. Find the x-intercept(s) at which f crosses the axis. Express the intercept(s) as
ordered pair(s).
A) none
B) 1
Page 73 of 123
C) 2
D) 3
E) 4 4
Step 3. Find the zero(s) at which f “flattens out”. Express the zero(s) as ordered pair(s).
A) none
B) 1
C) 2
D) 3
E) 4
29.
Find all zeros of the following polynomial. Be sure to find the appropriate number of
solutions (counting multiplicity) using the Linear Factors Theorem.
=
–
f(x) = x5 + x4 + 4×3 + 12×2 – 45x + 27
Answer: {
30.
Given that -2i is a zero, factor the following polynomial function completely. Use the
Conjugate Roots Theorem, if applicable.
=
–
–
f (x) = x4 – 7×3 + 14×2 – 28x + 40
Answer:
f(x) =
=
31.
Find all zeros of the following polynomial. Be sure to find the appropriate number of
solutions (counting multiplicity) using the Linear Factors Theorem.
=
–
f (x) = x3 – 12×2 + 37x – 40
–
Answer: {
32. Find equations for the vertical asymptotes, if any, for the following rational function.
34. Find equations for the horizontal asymptotes, if any, for the following rational function.
f(x) = -6
X
Answer:
35.
.
Consider the following rational function.
f(x) =
= -x2 +4
x3 – 1
Step 1. Find equations for the vertical asymptotes, if any, for the function.
Answer:
w
Step 2. Find equations for the horizontal or oblique asymptotes, if any, for the function.
Answer:
36.
Graph the following rational function.
f(x)
x + 6
=
x² – 64
Step 1. Plot the vertical asymptotes, if any, on the graph.
Number of Vertical Asymptotes:
A) None B) One C) Two
9 “78744 —–
responsible sources
FSC® C011825
Los Angeles I London I New Delhi | Singapore I Washington DC I Melbourne
SSAGE
X
Step 2. Plot the horizontal asymptotes, if any, on the graph.
Number of Horizontal Asymptotes:
A) None B) One C) Two