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

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Math

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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)

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