# Factor completely. z^5 - 4z^4 - 21z^3

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z^5 - 4z^4 - 21z^3

First, factor out z^3.

z^3(z^2 - 4z - 21)

Next, find two numbers whose product is -21 and sum is -4.

-7 * 3 = -21

-7 + 3 = -4

Now use these numbers to factor the trinomial.

z^3(z - 7)(z + 3)

**Final answer:****z^3(z - 7)(z + 3)**