Question: Consider the following polynomial function. \[ f(x) = (x + 5)^2(x - 1)^3(x - 2) \] Step 3 of 3:…

Consider the following polynomial function.

\[ f(x) = (x + 5)^2(x - 1)^3(x - 2) \]

Step 3 of 3: Find the zero(s) at which \( f \) “flattens out”. Express the zero(s) as ordered pair(s).

Answer

Select the number of zero(s) at which \( f \) “flattens out”.

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Solution

Step 1 Identify the zeros of the function. \[ f(x) = (x + 5)^2 (x - 1)^3 (x - 2) \] The zeros are \( x = -5 \), \( x = 1 \), and \( x = 2 \). Step 2 Determine the multiplicity of each zero. \[ \begin{cases} x = -5 \text{ has multiplicity } 2 & \\ x = 1 \text{ has multiplicity } 3 & \\ x = 2 \text{ has multiplicity } 1 & \end{cases} \] Zeros with multiplicity greater than or equal to 2 flatten out. Step 3 Express the zeros where \( f \) flattens out as ordered pairs. \[ (-5, 0), \ (1, 0) \]