Factor by grouping x3−4x2−4x+16
To factor by grouping, we group the terms as follows:
(x^3 - 4x^2) + (-4x + 16)
Now, we factor out the greatest common factor from each group:
x^2(x - 4) - 4(x - 4)
Next, notice that we have a common binomial factor, (x - 4), which we can factor out:
(x^2 - 4)(x - 4)
(x^2 - 4) is a difference of squares and can be factored further:
(x + 2)(x - 2)
Therefore, the factored form of x^3 - 4x^2 - 4x + 16 is (x + 2)(x - 2)(x - 4).