Question

which product of factors is equivalent to $x^{3}-x$?
a $x(x - 1)^{2}$
b $(1 + x)(x - 1)^{2}$
c $x(x - 1)(x + 1)$
d $(1 - x)(x - 1)^{2}$

Explanation:

Step1: Factor out the common factor

First, factor out \(x\) from \(x^{3}-x\). We get \(x(x^{2} - 1)\).

Step2: Use the difference - of - squares formula

Since \(a^{2}-b^{2}=(a - b)(a + b)\), and \(x^{2}-1=x^{2}-1^{2}\), then \(x^{2}-1=(x - 1)(x + 1)\). So \(x(x^{2}-1)=x(x - 1)(x + 1)\).

Answer:

C. \(x(x - 1)(x + 1)\)