High School

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------------------------------------------------ Solve the inequality:

[tex] x^3 + 3x^2 - 16x - 48 \ \textgreater \ 0 [/tex]

Answer :

Answer:

x > -4, x > -3, x > 4

Step-by-step explanation:

given inequality is:

x³ + 3x² - 16x - 48 > 0

x²(x + 3) - 16(x + 3) > 0

(x² - 16)(x + 3) > 0

(x² - 4²)(x + 3) > 0

(x - 4)(x + 4)(x + 3) > 0

as:

a² - b² = (a + b)(a - b)

i.e.

x - 4 > 0, x + 4 > 0, x + 3 > 0

x > -4, x > -3, x > 4

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