Factor by grouping x^3-4x^2- 4x+16
A (x+4)(x+2)
B (x+4)(x^2-4)
C (x+4)(x^2-4)
D (x-4)(x-2)
To factor the expression x^3 - 4x^2 - 4x + 16, we can use the method of grouping.
First, let's group the terms in pairs:
(x^3 - 4x^2) - (4x - 16)
Now, let's factor out the greatest common factor from each pair:
x^2(x - 4) - 4(x - 4)
Notice that we now have a common factor of (x - 4). Factoring this out, we get:
(x - 4)(x^2 - 4)
Next, we can further factor the expression x^2 - 4 as the difference of squares:
(x - 4)(x + 2)(x - 2)
So the factored form of the expression x^3 - 4x^2 - 4x + 16 is option C: (x + 4)(x^2 - 4).