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Chapter 0: Problem 128

Explain how to factor \(x^{3}+1\)

Short Answer

Expert verified
The factored form of \(x^{3}+1\) is \((x+1)(x^{2}-x+1)\).

Step by step solution

01

Identify the Values of a and b

We first need to identify the values of 'a' and 'b' from the equation \(x^{3}+1\). Here, \(a=x\) and \(b=1\).
02

Apply the Sum of Cubes Formula

Next, apply the sum of cubes formula: \(a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})\). With the values of 'a' and 'b' substituted, the formula equates to \(x^{3}+1^{3}=(x+1)(x^{2}-x*1+1^{2})\).
03

Simplify the Formula

Simplifying the equation further, we get \(x^{3}+1=(x+1)(x^{2}-x+1)\).

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