 8.4 Solving Polynomial & Rational Inequalities

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8.4 Solving Polynomial & Rational Inequalities

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

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

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

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]

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