SOLUTION: divide a.) {{{(15a^3-9a+a^2-24)/(6a^2)}}} b.) {{{(21x^3y^3-7xy^3-4xy^2-35y)/(-14xy^3)}}} c.) {{{(6x^6+32x^4+3x^3-14x^2-8)/(x^2+5)}}}

a.)  
b.)  
c.) 

The first two are DIVISION BY A MONOMIAL because the denominator has just one
term.
The third one is DIVISION BY A POLYNOMIAL because the denominator has more than
one term.

They are done differently.

a.)  

Put each term of the numerator over the denominator separately:

 

Then simplify each fraction as though it were a separate problem

 



b.)  

Put each term of the numerator over the denominator separately:



Remove the negative signs from the denominator using the rule of
multiplication and division of signs: 



Then simplify each fraction as though it were a separate problem:





c.) 

Here the denominator contains more than one term, so it is done by long
division. Be sure to insert 0 times any power of x that's missing:

                  6x⁴+0x³+ 2x²+ 3x¹- 24
x²+0x¹+5)6x⁶+0x⁵+32x⁴+3x³-14x²+ 0x¹-  8
         6x⁶+0x⁵+30x⁴
             0x⁵+ 2x⁴+3x³
             0x⁵+ 0x⁴+0x³
                  2x⁴+3x³-14x²
                  2x⁴+0x³+10x²
                      3x³-24x²+ 0x¹
                      3x³+ 0x²+15x¹   
                         -24x²-15x¹-  8
                         -24x²+ 0x¹-120
                              -15x¹+112 


Answer: 


Edwin