Factor the polynomial

[cchacon92]

Hello, for homework I was given \(\displaystyle x^{3}-27\) to factor and my answer can be written this way:

\(\displaystyle (x - A)(x^{2} + Bx + C)\)

I am being asked to find the value of A, B and C.
I am sure this is simpler than I think but it's perhaps the Bx that is confusing me as I haven't practiced a lot of these examples yet.

 

[MarkFL]

Hint: Write the polynomial as the difference of cubes $x^3-3^3$ then use the difference of cubes formula $a^3-b^3=(a-b)(a^2+ab+b^2)$.

 

[cchacon92]

Hint: Write the polynomial as the difference of cubes $x^3-3^3$ then use the difference of cubes formula $a^3-b^3=(a-b)(a^2+ab+b^2)$.

Alright, so I obtained \(\displaystyle (x -3)(x^{2} + 3x + C)\)

I still can't find C

 

[MarkFL]

In the formula I gave for the difference of cubes, you want to substitute $x$ for $a$, and $3$ for $b$. So what does this mean $C$ is equal to?

 

[cchacon92]

9 !! Great

 

[MarkFL]

Yes, good work!