Question 741552
<pre><font face = "consolas" color = "indigo" size = 4><b>
 4xz²-2xz-72x 

Factor out 2x

 2x(2z²-1z-36)

Now we need to factor what is in the parentheses,

    2z²-1z-36 

I will use the AC method

<pre><font face = "consolas" color = "indigo" size = 4><b>

Multiply the 2 by the 36 ignoring signs.  Get 72

Write down all the ways to have two positive integers
which have product 72, starting with 72*1

72*1
36*2
24*3
18*4
12*6
 9*8

Since the last sign in 2z²-1z-36 is -, SUBTRACT them,
and place the DIFFERENCE out beside that:

72*1   72-1=70
36*2   36-2=34
24*3   24-3=21
18*4   18-4=14
12*6   12-6= 6 
 9*8    9-8= 1

Now, again ignoring signs, we find in that list of
differences the coefficient of the middle term in 2z²-1z-36

So we replace the middle coefficient 1 by 9-8

2z²-1z-36
2z²-(9-8)z-36

Then we distribute to remove the parentheses:

2z²-9z+8z-36

Factor the first two terms 2z²-9z by taking out the
greatest common factor, z, getting z(2z-9)

Factor the last two terms +8z-36 by taking out the
greatest common factor, 4, getting +4(2z-9)

So we have

z(2z-9)+4(2z-9)

Notice that there is a common factor, <font color="red">(2z-9)</font>

z<font color="red">(2z-9)</font>+4<font color="red">(2z-9)</font>

which we can factor out leaving the z and the +4 to put 
in parentheses:

<font color="red">(2z-9)</font>(z+4)

So your final answer is:

 2x(2z-9)(z+4)

--------------------------------------------

For a lesson on how to factor trinomials 
 by the AC method, go here:

http://www.algebra.com/my/change_this_name32371.lesson?content_action=show_source

Edwin</pre>