# Thread: Help with Polynomial and Rational Function

1. ## Help with Polynomial and Rational Function

(1) For the function
h(x) = x3x2 – 17x -15,

use long division to determine which of the following are factors of h(x)

a) x + 5
b) x + 1
c) x + 3

(2) Determine the oblique asymptote of the graph of the function.

g(x) = x2 + 4x – 1 / x + 3

2. Originally Posted by topsquark
Oblique asymptotes are almost as easy as their horizontal counterparts.

As x gets larger and larger the $\displaystyle x^2$ term in the numerator dominates and the x term in the denominator dominates. So we have:
$\displaystyle \lim_{x \to large} \frac{x^2 + 4x - 1}{x + 3} \to \frac{x^2}{x} = x$

So the oblique asymptote is the line y = x.

You do the case for when x is large and negative.

-Dan
it seems to me that the oblique asymptote is y=x+1 and not y=x..

3. Originally Posted by kalagota
it seems to me that the oblique asymptote is y=x+1 and not y=x.
That is correct. To find the asymptote, you need to do a long division:
$\displaystyle \frac{x^2+4x-1}{x+3} = \frac{(x+3)(x+1)-4}{x+3} = x+1-\frac4{x+3}$. As $\displaystyle x\to\pm\infty$, this approaches x+1.

4. Here's a good link on polynomial long division: The Remainder Theorem

You may also want to try synthetic division (the method on the bottom of that page) to check your answer.