Factored form of \(f(x) = x^{3} -81x\) is equal to \(x(x+9)(x -9)\).
What is factored form?
" Factored form is defined as for the given polynomial product of the constant along with linear expressions."
Formula used
\(a^{2} -b^{2} =(a+ b)(a- b)\)
According to the question,
Given polynomial,
\(f(x) = x^{3} -81x\)
Simplify the given polynomial to get its factored form using formula,
\(x^{3} -81x\\\\= x(x^{2} -81)\\\\= x(x^{2} -9^{2} )\\\\= x(x+ 9)(x-9)\)
Hence, Option(C) is the correct answer.
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