Factor by grouping x3−4x2−4x+16
To factor by grouping, we can group the terms into pairs and factor out the greatest common factor from each pair.
Starting with the expression x^3 - 4x^2 - 4x + 16, we can group the first two terms and last two terms together:
(x^3 - 4x^2) + (-4x + 16)
Now we can 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) in both terms. We can factor out this common factor:
(x - 4)(x^2 - 4)
The expression x^2 - 4 is a difference of squares, so we can further factor it:
(x - 4)(x - 2)(x + 2)
Therefore, the factored form of the expression x^3 - 4x^2 - 4x + 16 is (x - 4)(x - 2)(x + 2).