How do you factor x^3+27?
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.
Let f(x) = x³ + 27
0 = 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
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.