1. 8.4 Solving Polynomial & Rational Inequalities

2. To solve a polynomial inequality: 1) Write in standard form
2) Find zeros
3) Plot zeros on number line
4) Choose test point in each interval to determine the sign
(factor, etc)
Ex 1) Solve 6x3 –10x2 < 24x
6x3 –10x2 – 24x < 0
2x(3x2 – 5x – 12) < 0
x = 0
want (–) values
(–)
(+)
(–)
(+) 3 –2
– 48 – –1
–6 – 1
6 – 10 – 24 4
384 – 160 – 96

3. (–∞, –4)  (–1, 1) Ex 2) Solve x3 + 4x2 < x + 4
want (–) values –4 –1 1 –5
(–)(–)(–)
(–) –2
(–)(–)(+)
(+)
(+)(–)(+)
(–) 2
(+)(+)(+)
(+)
(–∞, –4)  (–1, 1)

4. Ex 3) Graph in the coordinate plane
y > 3x3 – 5x + 1
Dotted line
Shade above
Use the strategies from Ch 7!! –
I.V.T. 1 3 3 –2 –1
I.V.T. 2 3 6 7 15
upper
bound –1 3 –3 –2 3
I.V.T. –2 3 –6 7
–13
lower
bound y x

5. Ex 4) Solve with the aid of a graph
Method 1
Find intersection pts
Method 2
Find zeros
Let’s have half of you try Method 1 and the other try Method 2
Where is parabola less than cube root?
[–1.6, 1.6]
Where is graph less than zero?
[–1.6, 1.6]

6. Homework
# Pg 409 #1, 6, 13, 18, 24, 29, 32, 35, 42, 43