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 \(3x(x - 1)(x + 1)\).
Other exercises in this chapter
Problem 64
Evaluate each expression in Exercises \(55-66,\) or indicate that the root is not a real number. $$\sqrt[5]{(-2)^{5}}$$
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Evaluate each algebraic expression for x = 2 and y = -5. $$|x|-|y|$$
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Write each number in decimal notation without the use of exponents. $$3.8 \times 10^{2}$$
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Simplify each complex rational expression. $$\frac{x-\frac{x}{x+3}}{x+2}$$
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