Factor by grouping x3−4x2−4x+16%0D%0A%0D%0A3%0D%0A−%0D%0A4%0D%0A%0D%0A2%0D%0A−%0D%0A4%0D%0A%0D%0A+%0D%0A16%0D%0A(1 point)
To factor by grouping, we need to group the terms in pairs and factor out the greatest common factor from each pair.
For the given expression: x^3 - 4x^2 - 4x + 16
Grouping the terms:
(x^3 - 4x^2) - (4x - 16)
Factor out the greatest common factor from each pair:
x^2(x - 4) - 4(x - 4)
Now, we have a common factor of (x - 4) in both terms, so we can factor it out:
(x^2 - 4)(x - 4)
Further simplifying, we can notice that (x^2 - 4) is a difference of squares, so we can factor it again:
(x - 2)(x + 2)(x - 4)
Therefore, the factored form of the expression x^3 - 4x^2 - 4x + 16 is (x - 2)(x + 2)(x - 4).