Factor by grouping x3−4x2−4x+16

Question

(x+4)(x+2)
(x+4)(x2−4)
(x−4)(x2−4)
(x−4)(x−2)

Answer 1

To factor by grouping, we divide the expression into two pairs:

First pair: x³ - 4x²
Second pair: -4x + 16

Now, we can factor out the common factor from each pair separately:

First pair: x²(x - 4)
Second pair: -4(x - 4)

Now, we notice that (x - 4) is a common factor between the two pairs, so we can factor it out:

(x - 4)(x² - 4)

We can also simplify further by recognizing that (x² - 4) is a difference of squares, which can be factored as:

(x - 4)(x + 2)(x - 2)

Therefore, the factored form of the expression x³ - 4x² - 4x + 16 is (x - 4)(x + 2)(x - 2).