iwanttogotostanford
  • iwanttogotostanford
PLZ HELP A
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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freckles
  • freckles
divide to find out
freckles
  • freckles
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 \[\frac{P(x)}{Q(x)}=ax+b+ \frac{R(x)}{Q(x)} \text{ where } P(x) \text{ is one more degree than } Q(x) \\ ax+b \text{ is the oblique asymptote }\]
freckles
  • freckles
R(x) represents the remainder function

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freckles
  • freckles
anyways you just have to divide and look at the quotient
mathmale
  • mathmale
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
freckles
  • freckles
if you don't like dividing let me know and I can show you away just by multiplying
freckles
  • freckles
it will also consist of your comparing both sides of an equation to determine coefficents
mathmale
  • mathmale
Please get started at the actual division: x^2+5x+6/x-4 (or, better yet, see below)\[\frac{ x^2+5x+6 }{ x-4 }\]
mathmale
  • mathmale
Use either long division or synthetic division. The problem's straightforward, so I'd recommend you use long div. Label your result with "y= "
freckles
  • freckles
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...
iwanttogotostanford
  • iwanttogotostanford
@freckles ok, got it! What would the final result be?:-)
iwanttogotostanford
  • iwanttogotostanford
y=x+9?
iwanttogotostanford
  • iwanttogotostanford
@freckles
mathmale
  • mathmale
Please explain where that 9 came from. Your x, in y=x+9, is fine.
mathmale
  • mathmale
I'd still like to see your work, whether you used long division or synthetic div.
iwanttogotostanford
  • iwanttogotostanford
I used synthetic division and go x+9 as my conclusion @mathmale
mathmale
  • mathmale
thank you for sharing your work. I tried it myself and got the same result.

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