What is 2x^3+5x^2<8x+20 ?

The solution to 2x^3+5x^2<8x+20 is x<-5/2 \lor-2<x<2

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2x^3+5x^2<8x+20

2 x^{3} + 5 x^{2} < 8 x + 20

x < - \frac{5}{2} or - 2 < x < 2

Interval Notation

(- \infty, - \frac{5}{2}) \cup (- 2, 2)

Decimal Notation

x < - 2.5 or - 2 < x < 2

Solution steps

2 x^{3} + 5 x^{2} < 8 x + 20

Rewrite in standard form

2 x^{3} + 5 x^{2} - 20 - 8 x < 0

Factor

2 x^{3} + 5 x^{2} - 20 - 8 x : (2 x + 5) (x + 2) (x - 2)

(2 x + 5) (x + 2) (x - 2) < 0

Identify the intervals

x < - \frac{5}{2} or - 2 < x < 2

6 k^{2} + 11 k - 46 = 0

(\frac{1}{2})^{4} \cdot (\frac{1}{2})^{2}

12 x^{2} + 19 x + 4

- 6 x - 6 = 103 x - 103

3 (2 y - 1) = 9