Question

Identify the factors of the expression x^3 +4x^2-16x-64.

Answer 1

Consider the following polynomial:

`x^3+4x^2-16x-64`

By grouping terms, we get that the above polynomial is equivalent to the following expression:

`(x^3+4x^2)+(-16x-64)`

Now, we can apply common factor:

`x^2(x^{}+4^{})-16(x+4)`

again, applying a common factor, we get:

`(x^2-16)(x+4)`

Note that the left factor is a difference of squares, therefore, the above expression is equivalent to:

`(x-4)(x+4)(x+4)`

this is equivalent to:

`(x-4)(x+4)^2`

So that, we can conclude that the factors of the given expression are:

`(x-4)`

and

`(x+4)^{2^{}}`

and we can conclude that:

`x^3+4x^2-16x-64=(x-4)(x+4)^2`