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
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, (2z-9)
z(2z-9)+4(2z-9)
which we can factor out leaving the z and the +4 to put
in parentheses:
(2z-9)(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
