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Chapter 6: Problem 114

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 a and b

In the given equation \(x^{3}+1\), \(a\) is \(x\) (since \(x^3\) is equivalent to \((x)^3\)) and \(b\) is 1 (since \(1\) is equivalent to \((1)^3\)).
02

Apply the sum of cubes formula

Substitute \(a\) and \(b\) into the sum of cubes factoring formula \(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\), which results in \((a + b)(a^2 - ab + b^2) = (x + 1)(x^2 - x*1 + 1^2)\)
03

Simplify the equation

Simplify the equation to get a simplified factored expression. The equation simplifies to \((x + 1)(x^{2} - x + 1)\)

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Most popular questions from this chapter

Factor completely. $$(x-7)^{2}-4 a^{2}$$

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$y^{3}+2 y^{2}-4 y-8$$

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$10 x^{4}+20 x^{3}+15 x^{2}$$

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