How do I factor x3 – 27?

Question

How do I factor the expression x³ – 27? (Note: x³ represents x raised to the third power, not three times x.)

Aisha Denesik · Accepted Answer

x^3 &ndash; 27x^3 &ndash; 3^3(x &ndash; 3)(x^2 + 3x + 9)Remember these formulas,x^3 + a^3 = (x + a)(x^2 &ndash; ax + a^2)x^3 &ndash; a^3 = (x &ndash; a)(x^2 + ax + a^2)2.) Not a big difference, just switch them,27 &ndash; x^33^3 &ndash; x^3(3 &ndash; x)(9 &ndash; 3x + x^2)

Anonymous · Answer

Factoring X 3

Dr. Xander Reichert PhD · Answer

x^3 – 27 = (x – 3) (x^2 + 3x + 9)
it is an example of special products called difference of cubes..
x^3 – 27 = x^3 – 3^3
applying the solution:
x^3 – y^3 = (x – y) (x^2 + xy + y^2)
it will become…
x^3 – 3^3 = (x – 3) (x^2 + 3x + 9)

Anonymous · Answer

You can factor a term like x^3 – a^3 as (x-a1)(x-a2)(x-a3), where a1, a2, a3 are the three cube roots of a^3, i.e. a, -a/2(1+i root(3)), and -a/2(1-i root(3)).  
Thus, x^3-27 factors into (x-3)(x+3/2((1+i root(3))(x+3/2((1-i root(3))
As to your second question, this is just the negative of the first expression, so you multiply the factorization I gave above by -1.
Al the answers above are correct, but mine is the only complete factorization.

Anonymous · Answer

The main formula is a^3 – b^ 3 = (a – b)(a^2 + ab + b^2)
We apply the same procedure here and plug in the respective values for “a” and “b”
So its: (x – 3)(x^2 + 3x + 9)
There it is…factored!

Anonymous · Answer

https://shorturl.im/axzRJ
x3 + 27 is the sum of cubes, so use the rule for factoring the sum of cubes: (x + 3)(x2 – 3x + 9)

Anonymous · Answer

difference of perfect cubesa^3 &ndash; b^3 = (a &ndash; b) (a^2 + ab + b^2)x^3 &ndash; 3^3(x &ndash; 3) (x^2 + 3x + 9)

Prof. Connor Towne MD · Answer

a^3 – b^3 = (a-b)(a^2+ab+b^2)
so:
x^3 – 27 = (x-3)(x^2 + 3x + 9)

Anonymous · Answer

x^3 – 27
x^3 – 3^3
(x – 3)(x^2 + 3x + 9)
x^3 + a^3 = (x + a)(x^2 – ax + a^2)
x^3 – a^3 = (x – a)(x^2 + ax + a^2)

Frank Bosco II · Answer

x3-27=0
=x3-3×2+3×2-9x+9x-27
=(x-3)(x2+3x+9)
x=3

Palma Emard

How do I factor x3 – 27?

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