# How do you factor #4x^3 + 36#?

##### 1 Answer

May 9, 2016

#### Answer:

#### Explanation:

First separate out the common scalar factor

#4x^3+36 = 4(x^3+9)#

Note that

We can still use the sum of cubes identity:

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

with

#x^3+9#

#=x^3+(root(3)(9))^3#

#=(x+root(3)(9))(x^2-x(root(3)(9))+(root(3)(9))^2)#

#=(x+root(3)(9))(x^2-root(3)(9)x+root(3)(81))#

#=(x+root(3)(9))(x^2-root(3)(9)x+3root(3)(3))#

So:

#4x^3+36 = 4(x+root(3)(9))(x^2-root(3)(9)x+3root(3)(3))#