What is x^3+4x^2>= 4x+16 ?

The solution to x^3+4x^2>= 4x+16 is -4 = 2

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x^3+4x^2>= 4x+16

x^{3} + 4 x^{2} \geq 4 x + 16

- 4 \leq x \leq - 2 or x \geq 2

Interval Notation

[- 4, - 2] \cup [2, \infty)

Solution steps

x^{3} + 4 x^{2} \geq 4 x + 16

Rewrite in standard form

x^{3} + 4 x^{2} - 16 - 4 x \geq 0

Factor

x^{3} + 4 x^{2} - 16 - 4 x : (x + 4) (x + 2) (x - 2)

(x + 4) (x + 2) (x - 2) \geq 0

Identify the intervals

- 4 \leq x \leq - 2 or x \geq 2

3 x - \frac{1}{2} = 1 \frac{1}{2}

4 x^{2} - 80 x = - 372

4 x^{2} - 25 x + 25

\frac{18 !}{( 18 - 3 ) !}

- 72

What is x^3+4x^2>= 4x+16 ?
The solution to x^3+4x^2>= 4x+16 is -4<= x<=-2\lor x>= 2