Factored form of [tex]f(x) = x^{3} -81x[/tex] is equal to [tex]x(x+9)(x -9)[/tex].
What is factored form?
" Factored form is defined as for the given polynomial product of the constant along with linear expressions."
Formula used
[tex]a^{2} -b^{2} =(a+ b)(a- b)[/tex]
According to the question,
Given polynomial,
[tex]f(x) = x^{3} -81x[/tex]
Simplify the given polynomial to get its factored form using formula,
[tex]x^{3} -81x\\\\= x(x^{2} -81)\\\\= x(x^{2} -9^{2} )\\\\= x(x+ 9)(x-9)[/tex]
Hence, Option(C) is the correct answer.
Learn more about factored form here
brainly.com/question/11522665
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