Question

which of the following describes the roots of the polynomial function (f(x) = (x+2)^2(x-4)(x+1)^3)?

-2 with multiplicity 2, 4 with multiplicity 1, and -1 with multiplicity 3
-2 with multiplicity 3, 4 with multiplicity 2, and -1 with multiplicity 4
2 with multiplicity 2, -4 with multiplicity 1, and 1 with multiplicity 3
2 with multiplicity 3, -4 with multiplicity 2, and 1 with multiplicity 4

Explanation:

Identify the roots of each linear factor

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Determine the multiplicity of each root

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Match with the correct option

$$ \text{The correct description is: } -2 \text{ with multiplicity } 2\text{, } 4 \text{ with multiplicity } 1\text{, and } -1 \text{ with multiplicity } 3 $$

Answer:

• (A) \(-2\) with multiplicity 2, 4 with multiplicity 1, and \(-1\) with multiplicity 3 (Correct answer)
• (B) \(-2\) with multiplicity 3, 4 with multiplicity 2, and \(-1\) with multiplicity 4
• (C) 2 with multiplicity 2, \(-4\) with multiplicity 1, and 1 with multiplicity 3
• (D) 2 with multiplicity 3, \(-4\) with multiplicity 2, and 1 with multiplicity 4