If \(f(x)=x^3\) and \(g(x)=x\), what is the factorized form of \((f-g)(x)\)?

Correct answer: \(x(x-1)(x+1)\)

\((f-g)(x)=f(x)-g(x)=x^3-x\). Taking \(x\) as the common factor gives \(x(x^2-1)\). Using the difference-of-squares identity \(x^2-1=(x-1)(x+1)\), the factorized form is \(x(x-1)(x+1)\). Option C is incorrect because \((x-1)\) is squared, so it does not equal \(x^3-x\). Exam tip: take out the common factor first, then apply \(a^2-b^2=(a-b)(a+b)\).