How the reverse operation for multiplying polynomial is called?

Asked May 20 '18 at 11:04

Active May 20 '18 at 11:12

Viewed 36 times

Say I have a polynomial and I want to know which components it consists of.

As an example, $$yx^2 + y^2 = 2y + 63 - 7x^2 \iff yx^2 + 7x^2 + y^2 - 2y - 63 = 0\\ \iff (y+7)(y+x^2-9) = 0 \iff \begin{cases} y = -7,\\y = 9 - x^2\end{cases}$$

There are some techniques for some easy equations, but is there a general algorithm for solving such things?

edited May 20 '18 at 11:12

achille hui

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asked May 20 '18 at 11:04

Arthur

You want to find its roots, which is precisely what the example is doing. – Bilbottom May 20 '18 at 11:06
Ok thanks. But how can one find them in the example? – Arthur May 20 '18 at 11:08
It's generally not a trivial process, and varies from polynomial to polynomial. Sometimes you can just notice the roots, sometimes you have to substitute values into the polynomial and see which ones give you zero, other types of polynomials have more generalised methods. What you've asked is actually a huge part of algebra because of how non-trivial it is. – Bilbottom May 20 '18 at 11:12
This is one example, and so is this. – Bilbottom May 20 '18 at 11:13
Consider searching for polynomial factorisation and you may find techniques that help you. – Bilbottom May 20 '18 at 11:14
Thank you Bill Wallis! :) – Arthur May 20 '18 at 11:16

How the reverse operation for multiplying polynomial is called?

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