What is the remainder when (x^3 +1)/(x^2 +3) is divided by (x^3 +1)/(x^2 +3)?

  • Thread starter mirandasatterley
  • Start date
In summary, the expression (x^3 +1)/(x^2 +3) cannot be simplified any further and cannot be factored. Its domain is all real numbers except for x = ±√3, and it has no real solutions. However, it can be graphed using a graphing calculator or software, resulting in a cubic curve with a vertical asymptote at x = ±√3.
  • #1
mirandasatterley
62
0
(x^3 +1)/(x^2 +3) = ?


_X______
X^2 + 3 / X^3 +1
- X^3 +3X
-----------
-3X +1
From here. I cannot figure out what to do.
 
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  • #2
Hint: your work is done. :wink:
 
  • #3
Second hint: the remainder, -3x+ 1 has lower degree than the divisor.

8/3= 2 with remainder 2 or 2+ 2/3, because the remainder, 2, is less than the divisor, 3.
 

1. What is the solution to (x^3 +1)/(x^2 +3)?

The solution to this expression is not a single number, but rather a polynomial expression of the form x + 3 + 1/(x^2 + 3). This is because the expression cannot be simplified any further.

2. Can the expression (x^3 +1)/(x^2 +3) be factored?

No, this expression cannot be factored further as it is already in its simplest form.

3. What is the domain of the expression (x^3 +1)/(x^2 +3)?

The domain of this expression is all real numbers except for x = ±√3, as these values would result in a division by zero which is undefined.

4. How many real solutions does the equation (x^3 +1)/(x^2 +3) = 0 have?

There are no real solutions to this equation as the expression (x^3 +1)/(x^2 +3) can never equal zero for any real value of x.

5. Can the expression (x^3 +1)/(x^2 +3) be graphed?

Yes, this expression can be graphed using a graphing calculator or software. The resulting graph would be a cubic curve with a vertical asymptote at x = ±√3.

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