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**8.4 Solving Polynomial & Rational Inequalities**

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**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

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**(–∞, –4) (–1, 1) Ex 2) Solve x3 + 4x2 < x + 4**

want (–) values –4 –1 1 –5 (–)(–)(–) (–) –2 (–)(–)(+) (+) (+)(–)(+) (–) 2 (+)(+)(+) (+) (–∞, –4) (–1, 1)

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**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

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**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]

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

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