How to divide a polynomial by a polynomial and a number

[azure sparrow]

how do I solve and equation where I need to divide a polynomial with a polynomial and a number (eg. (x^2 + x + 11) ÷ (x - 5))

[cunning minnow]

1. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
2. Wait patiently for a helper to come along.
3. Once someone helps you, say thank you and close the thread with:

   +close
   

4. Feel free to nominate the person for helper of the week in #helper-nominations
5. Do not ping the mods, unless someone is breaking the rules.
6. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[wheat goblet]

There are several approaches. I would do it in the following way.
Notice that x^2 + x + 11 = x(x + 1) + 11. We want x - 5, however, so:
x(x + 1) + 11 = x(x - 5 + 6) + 11 = x(x - 5) + 6x + 11
So:
(x^2 + x + 11)/(x - 5) = (x(x - 5) + 6x + 11)/(x - 5) = x + (6x + 11)/(x - 5)
We then do a similar thing for 6x + 11:
6x + 11 = 6(x - 5 + 5) + 11 = 6(x - 5) + 41
So:
(x^2 + x + 11)/(x - 5) = x + (6(x - 5) + 41)/(x - 5) = x + 6 + 41/(x - 5)

With enough practice those intermediate steps won't be necessary, and you would be able to do it like this:
(x^2 + x + 11)/(x - 5) = (x(x - 5) + 6x + 11)/(x - 5) = x + (6(x - 5) + 41)/(x - 5) = x + 6 + 41/(x - 5)

[azure sparrow]

thank you!

[long arrow]

there is a long division procedure too

and a synthetic div method

its difficult to explain by text

[zinc basin]

Better to watch a video for that

YouTube would do

[azure sparrow]

ok. thank you for the information guys!

+close