Questions: Solve the following inequality. [ (x-8)(x-2)(x+4) leq 0 ] Write your answer as an interval or union of intervals. If there is no real solution, click on "No solution".

Solve the following inequality. [ (x-8)(x-2)(x+4) leq 0 ] Write your answer as an interval or union of intervals. If there is no real solution, click on "No solution".
Transcript text: Solve the following inequality. \[ (x-8)(x-2)(x+4) \leq 0 \] Write your answer as an interval or union of intervals. If there is no real solution, click on "No solution".
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Solution

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Solution Steps

Step 1: Find the Real Zeros

The real zeros of the polynomial inequality are: -4, 2, 8.

Step 2: Test Intervals

Interval 1: (-oo, -4), Sign: - Interval 2: (-4, 2), Sign: + Interval 3: (2, 8), Sign: - Interval 4: (8, oo), Sign: +

Step 3: Determine the Solution Set

The solution set based on the inequality symbol '≤' is: [-oo, -4] ∪ [2, 8].

Final Answer:

The solution to the polynomial inequality is: [-oo, -4] ∪ [2, 8].

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