Question

factor -8z³ - 24z² - 18z completely.

Explanation:

Step1: Factor out common term

First, factor out the greatest common factor (GCF) from the three terms. The GCF of \(-8z^3\), \(-24z^2\), and \(-18z\) is \(-2z\).
$$-8z^3 - 24z^2 - 18z=-2z(4z^2 + 12z + 9)$$

Step2: Factor the quadratic

Now, factor the quadratic \(4z^2 + 12z + 9\). Notice that it is a perfect square trinomial since \(4z^2=(2z)^2\), \(9 = 3^2\), and \(12z = 2\times(2z)\times3\). So, \(4z^2 + 12z + 9=(2z + 3)^2\).

Answer:

\(-2z(2z + 3)^2\)