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)
Answers
(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)
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).