What is the solution to x^3 +4x^2 > x + 4
2 answers:
Answer:
B) −4<x<−1 or x>1
Inequality Form: −4<x<−1 or x>1
Interval Notation: (−4,−1) ∪ (1,∞)
Step-by-step explanation:
Solve: x^3 + 4x^2 > x + 4
Subtract x from both sides of the inequality.
x^3 + 4x^2 − x > 4
Convert the inequality to an equation.
x^3 + 4x^2 − x = 4
Move 4 to the left side of the equation by subtracting it from both sides.
x^3 + 4x^
2 − x − 4 = 0
Factor the left side of the equation
(x + 4)(x + 1)(x − 1) = 0
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to 0
x + 4 = 0
x + 1 = 0
x − 1 = 0
Set x + 4 equal to 0 and solve for x
x = −4
Set x + 1 equal to 0 and solve for x
x = −1
Set x + -1 equal to 0 and solve for x
x = 1
The final solution is all the values that make (x + 4)(x + 1)(x − 1) = 0 true
x = −4, −1, 1
Use each root to create test intervals.
x < −4
−4 < x < −1
−1 < x < 1
x > 1
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the
inequality.
x < −4 ←False
−4 < x < −1 ←True
−1 < x < 1 ←False
x > 1 ←True
The solution consists of all of the true intervals.
−4 < x < −1 x > 1
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