Please factor the following

Question

x^3 + 27.
I cannot seem to grasp the concept

Thank you

Answer 1

a^3 + b^3 = (a+b)(a^2-ab+b^2)

so, x^3+3^3 = (x+3)(x^2-3x+9)

Answer 2

First, you can take the cubed root of x^3 to get x. Second, you can take the cubed root of 27 to get 3.

So, let's start by dividing x^3 + 27 by x + 3:

.......x^2 - 3x + 9
x + 3 )x^3 + 27
.......x^3 + 3x^2-->change signs
........... - 3x^2 + 27
........... - 3x^2 - 9x-->change signs
.....................9x + 27
.....................9x + 27-->change signs
...........................0-->no remainder

Factors are:
(x + 3) (x^2 − 3x + 9)

I hope this will help.