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Simplify using long division

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2 Answers

Nkeiruka, we do this just like we do long division with whole numbers.  Let's see what we can come up with.
 
First, we have to put things in order: 12y^3 + 12y^2 - 39y +15
 
How many times does 2y go into 12y^3?  6y^2, right?  6y^2(2y+5)= 12y^3+30y^2.
 
   12y^3 - 12y^2
-  12y^3 +30y^2
______________
              -18y^2
 
Bring down the -39y, so you have -18y^2 - 39y.  How many times does 2y go into -18y?  -9y, right? -9y(2y+5)= -18y^2-45y
 
   -18y^2 - 39y
-  -18y^2 - 45y
______________
                 6y
 
Bring down the 15 to make 6y+15
 
How many times does 2y go into 6y?  3, so 3(2y+5)= 6y+15
 
   6y + 15
-  6y + 15
__________
            0
 
You final answer is 6y^2 - 9y + 3.
 
Check your answer and do the same for the second problem.

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