Question
Find the roots of the factored polynomial. \[ \begin{array}{l}(x-3)^{3} \\ \text { Write your answer as a list of values separated by comma } \\ x=\end{array} \]
Ask by Bolton Lee. in the United States
Feb 03,2025
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Answer
\[ x = 3 \]
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The Deep Dive
To find the roots of the factored polynomial \((x-3)^{3}\), we set the expression equal to zero: \[ (x-3)^{3} = 0. \] The root occurs when the expression inside the parentheses is equal to zero. Therefore, we have: \[ x - 3 = 0 \implies x = 3. \] Since the factor \((x-3)\) has an exponent of 3, the root \(x = 3\) has a multiplicity of 3. Thus, the root is: \[ x = 3, 3, 3. \] In a simpler format, we can state the roots as: \(x = 3.\)