5
QuizMultiple Choice

Composition of Functions and Modeling — Unit test

Question 5 • GA-GSE Pre-Calculus

What is the solution to (x – 3)3(x + 1)(x – 2) ≤ 0?

Answer
A
(–ꝏ, –1) U (2, 3)
B
(–ꝏ, –1] U [2, 3]
C
(–1, 2) U (3, ꝏ)
D
[–1, 2] U [3, ꝏ)

Explanation

The zeros are x = −1, 2, and 3. Each has odd multiplicity, so the expression changes sign at each zero; since it is positive for x > 3, it is negative on (2, 3) and (−∞, −1). Because the inequality includes equality, include all three zeros, giving (−∞, −1] ∪ [2, 3], choice B.

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