SOLUTION: Obtain the quotient and remainder when h(z)=4z^2+2z^2+3z-5 is divided by 2z+3

I don't want to do your problem for you.  I have worked yours and have
noticed what is probably the reason you had trouble with this one.  It
involves a situation where one whole number does not divide evenly into
another and we must use a fraction or decimal instead of a whole number.

So here is another problem exactly like yours that involves the same
situation:

Obtain the quotient and remainder when h(z)=12z³+3z²+7z-2 is divided by
4z+5.

You probably got this far with your long division problem correspondingly:

               3z² -  3z        
4z + 5)12z³ +  3z² +  7z -  2
       12z³ + 15z²
             -12z² +  7z
             -12z² - 15z 
                     22z -  2
                       
                                         

but were stumped because 4z does not divide evenly into 22z.

So what we do is divide 22 by 4 and get the decimal 5.5 and 
finish like this:

               3z² -  3z +  5.5
4z + 5)12z³ +  3z² +  7z -  2
       12z³ + 15z²
             -12z² +  7z
             -12z² - 15z 
                     22z -  2
                     22z + 27.5  
                          -29.5

The quotient is 3z²-3z+5.5 and the remainder is -29.5.

Now use this as a guide and do your long division problem
the same way.  If you have trouble, ask me in the form at
the bottom and I'll get back to you by email.  There is 
never any charge.  

Edwin