Problem 65

Question

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

Step-by-Step Solution

Verified
Answer
The fully factored form of the polynomial \(3x^3 - 3x\) is \(3x(x - 1)(x + 1)\).
1Step 1: Identify the common factor
In the given polynomial \(3x^3 - 3x\), the common factor is \(3x\).
2Step 2: Apply the factoring process
Factor out the common factor \(3x\) from the given polynomial. The result will be \(3x(x^2 - 1)\).
3Step 3: Factor the remaining polynomial
Remember that \(x^2 - 1\) is a difference of squares and can be factored as \((x - 1)(x + 1)\). Therefore, the fully factored form of the given polynomial is \(3x(x - 1)(x + 1)\).