8.4 Solving Polynomial & Rational Inequalities

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 (–) (–) (+) (+) 0 3 –2 – 48 – 40 + 48 4 384 – 160 – 96 –1 –6 – 10 + 24 1 6 – 10 – 24

3. Ex 2) Solve x3 + 4x2 < x + 4 x3 + 4x2 – x – 4 < 0 x2(x + 4) – 1(x + 4) < 0 (x2 – 1)(x + 4) < 0 (x + 1)(x – 1)(x + 4) < 0 x = –1, 1, –4 • want (–) values –4 –1 1 –5 (–)(–)(–) (–) –2 (–)(–)(+) (+) 0 (+)(–)(+) (–) 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!! 0 3 0 –5 1 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 #804 Pg 409 #1, 6, 13, 18, 24, 29, 32, 35, 42, 43