The factor of the expression is [tex](x-3)\left(x^{2}+3 x+9\right)$[/tex].
Factors
Given:
[tex]x^{3}-27$[/tex]
Rewrite 27 as [tex]$3^{3}$[/tex]
then, we get [tex]x^{3}-3^{3}$[/tex]
Since both terms are perfect cubes, factor using the difference of cubes formula, we get
[tex]$a^{3}-b^{3}=(a-b)\left(a^{2}+a b+b^{2}\right)$[/tex]
where a = x and b
[tex]&(x-3)\left(x^{2}+x \cdot 3+3^{2}\right)[/tex]
Simplifying the given equation as,
Move 3 to the left of x.
[tex](x-3)\left(x^{2}+3 x+3^{2}\right)$[/tex]
Raise 3 to the power of 2.
[tex](x-3)\left(x^{2}+3 x+9\right)$[/tex]
Therefore, the factor of the expression is
[tex](x-3)\left(x^{2}+3 x+9\right)$[/tex].
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