SOLUTION: I am having trouble with factoring and solving. Please help. I will greatly appreciate it. Please show work. Factor completely. If the polynomial is prime, state this. Factor

Don't list a bunch of problems.  We will only do one.

Factor completely by grouping. 


Factor out -6, remembering that when you factor out 
a negative number, all the signs change inside the
parentheses.



I'll do some coloring:



Ignoring signs at first, and just using absolute values,
multiply the red 6 by the green 6, getting 36.

Now write down all the ways of two integers
which multiply to give 36:

36*1 = 36
18*2 = 36
12*3 = 36
 9*4 = 36
 6*6 = 36

Now since the sign before the green 6 is -, out
beside those we SUBTRACT the two factors. (If that sign
has been + we would have added them):

36*1 = 36   36-1=35
18*2 = 36   18-2=16
12*3 = 36   12-3= 9 
 9*4 = 36    9-4= 5
 6*6 = 36    6-6= 0

Now we look in the right hand column to see if we can find
the absolute value of the coefficient of the middle term of



which is 5, which I have colored green.

Now replace the 5x by 9x-4x 



Now I'll do some re-coloring:



Out of the two red terms factor out a 3x



Now out of the remaining black terms, factor out ,
remembering that when you factor out a negative you change
the signs inside the parentheses:



Now I'll do some more re-coloring



Notice that the green parentheses are the same,
and you can factor them out  just as you would
factor out just a single letter or number.  When you do you just
put the remaining black factors inside a parentheses:



or just



Edwin