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Chapter 0: Problem 65

Factor completely, or state that the polynomial is prime. $$3 x^{3}-3 x$$

Short Answer

Expert verified
The completely factored form of \(3x^3 - 3x\) is \(3x (x - 1) (x + 1)\).

Step by step solution

01

Identify the Greatest Common Factor (GCF)

Observe the two terms in the polynomial, \(3x^3\) and \( -3x\). The greatest common factor here is \(3x\).
02

Apply the GCF

Divide each term of the polynomial by the GCF, which results in \(x^2 - 1\). This gives us the factored form as \(3x (x^2 - 1)\).
03

Factor Further if Possible

The expression \(x^2 - 1\) is a difference of squares, it can be factored further as \((x - 1)(x + 1)\). Thus, the completely factored form of the given expression would be \(3x (x - 1)(x + 1)\).

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