# How do you factor completely #4x^3-16x^2-9x+36#?

##### 1 Answer

Feb 1, 2017

#### Explanation:

The difference of squares identity can be written:

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

We will use this with

#4x^3-16x^2-9x+36 = (4x^3-16x^2)-(9x-36)#

#color(white)(4x^3-16x^2-9x+36) = 4x^2(x-4)-9(x-4)#

#color(white)(4x^3-16x^2-9x+36) = (4x^2-9)(x-4)#

#color(white)(4x^3-16x^2-9x+36) = ((2x)^2-3^2)(x-4)#

#color(white)(4x^3-16x^2-9x+36) = (2x-3)(2x+3)(x-4)#