[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]
What is the factored form of 1,458x³ − 2?
A. 2(9x − 1)(81x² + 9x + 1)
B. 2(9x + 1)(81x² − 9x + 1)
C. (9x − 2)(81x² + 18x + 4)
D. (9x + 2)(81x² − 18x + 4)
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex] \sf \: 1458 x ^ { 3 } - 2[/tex]
Factor out 2 (common factor).
[tex] \sf \: 2\left(729x^{3}-1\right) [/tex]
Consider [tex]729x^{3}-1[/tex]. Rewrite [tex]729x^{3}-1[/tex] as [tex]\left(9x\right)^{3}-1^{3}[/tex]. The difference of cubes can be factored using the rule: [tex]a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right)[/tex].
[tex] \sf\left(9x-1\right)\left(81x^{2}+9x+1\right) [/tex]
Rewrite the complete factored expression. Polynomial 81x²+9x+1 is not factored as it does not have any rational roots.
[tex] \boxed{ \boxed{ \bf A) \: \: 2\left(9x-1\right)\left(81x^{2}+9x+1\right) }}[/tex]
