# What are the roots of the equation #x^3 +4x^2-4x- 16=0#?

##### 2 Answers

The roots are:

#x = 2# ,#x = -2# and#x=-4#

#### Explanation:

The difference of squares identity can be written:

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

We use this with

Given:

#x^3+4x^2-4x-16 = 0#

Note that the ratio between the first and second terms is the same as the ratio between the third and fourth terms, so this cubic factors by grouping:

#0 = x^3+4x^2-4x-16#

#color(white)(0) = (x^3+4x^2)-(4x+16)#

#color(white)(0) = x^2(x+4)-4(x+4)#

#color(white)(0) = (x^2-4)(x+4)#

#color(white)(0) = (x^2-2^2)(x+4)#

#color(white)(0) = (x-2)(x+2)(x+4)#

Hence the roots are:

#x = 2# ,#x = -2# and#x=-4#

#### Explanation:

(i.e.

Dividing

which factors using standard operations as:

Therefore