Why is (2x^2)/(x^2+1) not dividing evenly?

In summary, when dividing (2x^2)/(x^2+1), make sure the divisor is outside when doing long division. The correct quotient is 2 + (-2)/(x^2 + 1) and a check can be done by multiplying the quotient by the divisor to get 2x^2.
  • #1
questionasker1
6
0
I've looked examples up online and I just can't figure out what to do exactly when I have (2x^2)/(x^2+1), for some stupid reason that was probably the work of satan, EVERY problem on the internet only has the lead coefficient of the numerator equal to or less than that in the denominator and when I divide I just don't get the answer I am suppose to get.

...(1/2)?
2x^2...|(x^2+1)``````
2x^2 goes into x^2 one half times according to my mathematics, but somehow that answer doesn't work, somehow 2x^2 goes into x^2 twice.
 
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  • #2
questionasker1 said:
I've looked examples up online and I just can't figure out what to do exactly when I have (2x^2)/(x^2+1), for some stupid reason that was probably the work of satan, EVERY problem on the internet only has the lead coefficient of the numerator equal to or less than that in the denominator and when I divide I just don't get the answer I am suppose to get.

...(1/2)?
2x^2...|(x^2+1)``````
2x^2 goes into x^2 one half times according to my mathematics, but somehow that answer doesn't work, somehow 2x^2 goes into x^2 twice.
You're doing the division backwards. The divisor is x2 + 1, so it should be outside when you do the long division. Your quotient should be 2 + (-2)/(x2 + 1).

As a check, multiply the quotient ( 2 + (-2)/(x2 + 1) ) by the divisor ( x2 + 1 ), and you'll get 2x2.
 
  • #3
Ok that seemed to solve it, thanks.
 

1. What is polynomial long division?

Polynomial long division is a method used to divide two polynomials. It involves dividing the terms of the dividend (the polynomial being divided) by the terms of the divisor (the polynomial doing the dividing) and finding the quotient and remainder.

2. How is polynomial long division different from regular long division?

Polynomial long division is different from regular long division in that it deals with polynomials, which are expressions with variables and exponents, rather than just numbers. In polynomial long division, the terms of the dividend and divisor are divided based on their degrees (the highest exponent) and the quotient and remainder are expressed as polynomials.

3. Why is polynomial long division important?

Polynomial long division is important because it allows us to solve equations involving polynomials, which are commonly used in mathematics, science, and engineering. It also helps us simplify and factor polynomials, which is useful in solving more complex problems.

4. What are the steps for polynomial long division?

The steps for polynomial long division are as follows:
1. Arrange the dividend and divisor in descending order of degree.
2. Divide the first term of the dividend by the first term of the divisor to get the first term of the quotient.
3. Multiply the first term of the quotient by the entire divisor and subtract it from the dividend.
4. Bring down the next term of the dividend and repeat the process until all terms have been used.
5. The final answer will be the quotient plus the remainder over the divisor.

5. What are some common mistakes to avoid when using polynomial long division?

Some common mistakes to avoid when using polynomial long division include:
- Forgetting to arrange the terms in descending order of degree.
- Making errors in the division and subtraction steps.
- Not checking the final answer for accuracy.
To avoid these mistakes, it is important to be organized, double-check your work, and practice regularly to improve your skills.

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