Third-degree equations

Third-degree equation An equation in which the unknown appears at most as a third-degree superscript, z.B.

There are different kinds of third-degree equations. I would like to show you some examples and the steps that are necessary to solve them.

and number


  1. You divide by the number that comes before the alt="x^3" width="18" height="17" />standing and you already have the alt="x^3 width="18" height="17" />alone.
  2. You take the third root on both sides of the equation and you have found the solution.


  • In this kind of equation there is only and number.
  • If you take the third root, there is only one result.
  • You can also take the third root from negative numbers.



  1. You have to factor out one and then you can look at the two parts separately.
  2. The first solution is therefore and with the parenthesis you then have to calculate further.
  3. You can then calculate the solutions of the brackets with the midnight formula.


  • In each "element" there is an .
  • To solve this you need the theorem of the zero product and then the midnight/abc formula

Polynomial Division

Find first solution by trial and error or with the GTR.

\polyset{vars=x, style=C, delims={(}{)}} \polylongdiv{(x+5)(x^2+x-2)}{x+5}

a=1; b=1; c=-2


  1. You have to find one by trial and error or with the help of your GTR.
  2. You write down the equation and divide it by "the opposite" of your solution – if you have a negative number you have to divide by number and vice versa.
  3. Now divide that by that and write that after the equal sign, then write that with minus under the one on the left side and take that times the and write that with minus next to the one in the 2. Line and subtract both from each other. It remains and you now bring this down and the game starts all over again.
  4. Your result you put into the mid-after formula and then have three results at the end.


  • In this kind of equation you have , , and a number.
  • You need for solving the polynomial division and the midnight formula.

Do you know equations of third degree, which you can not solve or where you have difficulties in solving? Write it to me in the comment. Gladly I help you also about my online tutoring or my math tutoring on site.

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