# How do you divide #(3a^3+17a^2+12a-5)/(a+5)#?

##### 1 Answer

#### Explanation:

First, let's split the top polynomial up into "multiples" of the bottom polynomial. To see what I mean, let's first try to take care of the

We can see that

#3a^2(a+5) = 3a^3+15a^2# . So, let's separate this from our polynomial:

#3a^3 + 17a^2 + 12a - 5#

#(3a^3+15a^2) + 2a^2+12a-5#

#3a^2(a+5) + 2a^2+12a-5#

See how this "gets rid of" the

We can see that

#2a(a+5) = 2a^2 + 10a# .

#3a^2(a+5) + (2a^2+10a) + 2a-5#

#3a^2(a+5) + 2a(a+5)+ 2a-5#

The next highest term to deal with is the

We can see that

#2(a+5) = 2a+10# .

#3a^2(a+5) + 2a(a+5)+ (2a+10) -15#

#3a^2(a+5) + 2a(a+5)+ 2(a+5) - 15#

We can't do anything about the

Finally, let's divide everything by

#(3a^3+17a^2+12a-5)/(a+5) #

#= (3a^2(a+5) + 2a(a+5)+ 2(a+5) - 15)/(a+5)#

#= 3a^2+2a+2 - 15/(a+5)#

*Final Answer*