# How do you factor x^3+27?

##### 2 Answers

Because factoring x^3+27 is the same as finding where the graph passes through the x axis, we can just set the equation equal to zero and solve.

#### Explanation:

Let f(x) = x³ + 27

0 = x³ + 27

x³= -27

x = -3

This means that x = -3 is the only zero of the graph of f(x). Since we know

We get the second factor to be

Therefore,

#### Explanation:

The sum of cubes identity can be written:

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

Note that both

#x^3+27 = x^3+3^3#

#color(white)(x^3+27) = (x+3)(x^2-3x+3^2)#

#color(white)(x^3+27) = (x+3)(x^2-3x+9)#

The remaining quadratic has no simpler linear factors with Real coefficients.