Factor x^3-12x

Problem

x3−12*x

Solution

1. Identify the greatest common factor (GCF) of the terms in the expression.

2. Factor out the GCF, which is x from both terms.

3. Rewrite the expression as a product of the GCF and the remaining binomial.

4. Check if the resulting binomial x2−12 can be factored further over the integers. Since 12 is not a perfect square, the expression is fully factored over the set of rational numbers.

Final Answer

x3−12*x=x*(x2−12)

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