2006-07-08 14:31:03 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
This is a heavy one. There is no general solution.
When you know x-a is a factor, then you can go on with
(original polynomial) / (x-a) = (a polynomial one degree lower)
2006-07-08 18:56:18 · answer #1 · answered by Thermo 6 · 1⤊ 0⤋
If you write a polynomial as the product of two or more polynomials, you have factored the polynomial. Here is an example: x cubed - 3x squared - 2x + 6 = ( x-3)(x squared - 2)
The polynomials x-3 and x squared - 2 are called factors of the polynomial x cubed - 3x squared - 2x + 6 . Note that the degrees of the factors, 1 and 2, respectively, add up to the degree 3 of the polynomial we started with. Thus factoring breaks up a complicated polynomial into easier, lower degree pieces.
We are not completely done; we can do better: we can factor
x cubed - 3x squared - 2x + 6 = (x - 3)(x + square root of 2)(x- square root of 2)
We have now factored the polynomial into three linear (=degree 1) polynomials. Linear polynomials are the easiest polynomials. We can't do any better. Whenever we cannot factor any further, we say we have factored the polynomial completely.
2006-07-08 21:53:54 · answer #2 · answered by capejerry 1 · 0⤊ 0⤋
One cheat is to solve the equation for the polynomial equal to zero. If the roots are x1, x2, ..., then the polynomial can be represented as (x-x1)(x-x2) ... et cetera. But one is usually interested in factoring the polynomial in order to find the roots, so this won't help. Other responders have addressed the question for those cases.
2006-07-08 22:27:01 · answer #3 · answered by Anonymous · 0⤊ 0⤋
there are many tricks depending on the order of the polynomial. "order" of a polynomial is the largest exponent. that is x^2 + 3x + 4 is a 2nd order polynomial while x^5 -x^2 +3x +4 is a fifth order polynomial.
a very powerful method is called synthetic division. it is very simple and algorithmic. i will not explain it here but do a google search and you'll probably find several sites that have examples.
2006-07-08 21:41:12 · answer #4 · answered by cp_exit_105 4 · 0⤊ 0⤋
Wikipedia has a great page explaining how to do synthetic divison with step by step instructions. This is helpful if you think you have found a factor. If it divides cleanly then you have definitely found one factor of the polynomial.
2006-07-08 22:20:13 · answer #5 · answered by insideoutsock 3 · 0⤊ 0⤋
the two best ways r horners synthetic division and taylors theorem
2006-07-09 01:03:29 · answer #6 · answered by Anonymous · 0⤊ 0⤋
haha. You post it on here and have someone else do it for you. :P (I'm not speaking from expirience.)
2006-07-08 21:46:51 · answer #7 · answered by agfreak90 4 · 0⤊ 0⤋