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(x+4)(x+2)%0D%0A(%0D%0A%0D%0A+%0D%0A4%0D%0A)%0D%0A(%0D%0A%0D%0A+%0D%0A2%0D%0A)%0D%0Aopen paren x plus 4 close paren times open paren x plus 2 close paren%0D%0A%0D%0A(x+4)(x2−4)%0D%0A(%0D%0A%0D%0A+%0D%0A4%0D%0A)%0D%0A(%0D%0A%0D%0A2%0D%0A−%0D%0A4%0D%0A)%0D%0Aopen paren x plus 4 close paren times open paren x squared minus 4 close paren%0D%0A%0D%0A(x−4)(x2−4)%0D%0A(%0D%0A%0D%0A−%0D%0A4%0D%0A)%0D%0A(%0D%0A%0D%0A2%0D%0A−%0D%0A4%0D%0A)%0D%0Aopen paren x minus 4 close paren times open paren x squared minus 4 close paren%0D%0A%0D%0A(x−4)(x−2)

Answer 1

To factor the expression x^3 - 4x^2 - 4x + 16 by grouping, we can group the terms as follows:

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

Now, we can 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 of (x - 4), so we can factor it out:

(x^2 - 4)(x - 4)

Finally, we can factor the difference of squares, x^2 - 4, as (x + 2)(x - 2):

(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).