Help in Algebra 2 for medal? Thanks!!!

Question

lexipoo1998 · Answer

Identify the oblique asymptote of f(x) = quantity 3 x squared plus 2x minus 5 over quantity x minus 4

anonymous · Answer

I just want to make sure that I interpreted the equation properly.  Is it 
$$\large\frac{3x^2+2x-5}{x-4}?$$

lexipoo1998 · Answer

Yes that is it

lexipoo1998 · Answer

These are my answer choices

 y = 0 

 y = 3x – 10 

 y = 3x + 14 

 No Oblique Asymptote

anonymous · Answer

Since the degree of the numerator of your rational function (which is 2) is EXACTLY one more than the degree of the denominator (which is 1), we know for a fact that an oblique asymptote exists.  Now, to compute it, you will either have to use long division or synthetic division to rewrite your function.  The quotient would then be the equation of your oblique asymptote.  You can see the long division process below.

|dw:1386336146101:dw|

Therefore, the oblique asymptote is $\large y=3x+14$.  

Does this make sense?