Question

PLZ HELP A

Answer 1

divide to find out

Answer 2

you will oblique asymptote when the deg of the top is one more than the deg of the bottom
Let P and Q be polynomials then
\[\frac{P(x)}{Q(x)}=ax+b+ \frac{R(x)}{Q(x)} \text{ where } P(x) \text{ is one more degree than } Q(x) \\ ax+b \text{ is the oblique asymptote }\]

Answer 3

R(x) represents the remainder function

Answer 4

anyways you just have to divide and look at the quotient

Answer 5

Note: you can tell immediately that this function has a slant asymptote because the order of the numerator (2) is 1 greater than that of the denominator (1).

A slant asymptote is a line, remember, a first-order function: y=mx + b

Answer 6

if you don't like dividing let me know and I can show you away just by multiplying

Answer 7

it will also consist of your comparing both sides of an equation to determine coefficents

Answer 8

Please get started at the actual division: x^2+5x+6/x-4 (or, better yet, see below)\[\frac{ x^2+5x+6 }{ x-4 }\]

Answer 9

Use either long division or synthetic division. The problem's straightforward, so I'd recommend you use long div. Label your result with "y= "

Answer 10

well what I was suggesting also beside division was the following:
\[\frac{x^2+5x+6}{x-4}=ax+b+\frac{R(x)}{x-4} \\ \text{ we know the that } R(x) \\ \text{ is one degree less than } x-4 \\ \text{ So that means } R(x) \text{ is a constant function } \\ \text{ So let's let} R(x)=R \\ \\ \frac{x^2+5x+6}{x-4}=ax+b+\frac{R}{x-4} \\ \text{ multiply both sides by } x-4 \\ x^2+5x+6=(ax+b)(x-4)+R \]
now expand and collect like terms on right hand side
then you compare coefficients of both sides
this is an equality so that means you have to pick a, b, and R such that you have the same amount of x^2 on both sides, the same amount of x on both sides, and the same amount of constant on both side
I mention this way because I think it is a pretty useful was to learn
and I think it is fun...

Answer 11

@freckles ok, got it! What would the final result be?:-)

Answer 12

y=x+9?

Answer 13

@freckles

Answer 14

Please explain where that 9 came from. Your x, in y=x+9, is fine.

Answer 15

I'd still like to see your work, whether you used long division or synthetic div.

Answer 16

I used synthetic division and go x+9 as my conclusion @mathmale

Answer 17

thank you for sharing your work. I tried it myself and got the same result.