Methods of polynomials division
$begingroup$
How does the division method for polynomial discovered. I have read about ruffini method, it needs divisor to be binomial and linear, I tried to understand horner's method, but couldn't. but methods are traditional and different from what I am doing (like this one below):
How this method (image one) came from earlier methods?
polynomials
$endgroup$
add a comment |
$begingroup$
How does the division method for polynomial discovered. I have read about ruffini method, it needs divisor to be binomial and linear, I tried to understand horner's method, but couldn't. but methods are traditional and different from what I am doing (like this one below):
How this method (image one) came from earlier methods?
polynomials
$endgroup$
1
$begingroup$
Do You remember the method to divide integers by hand? Polymomial rings have essentially the same structure as the ring of integers.
$endgroup$
– Peter Melech
Dec 30 '18 at 14:24
$begingroup$
Is this fact known in earlier time, then what are horner's and ruffini method
$endgroup$
– user629353
Dec 30 '18 at 14:29
$begingroup$
Did ruffini know that dividing polynomials is similar to how integer division works
$endgroup$
– user629353
Dec 30 '18 at 14:50
$begingroup$
How it came to know that polynomial division is similar to as in integer case
$endgroup$
– user629353
Dec 30 '18 at 14:58
$begingroup$
I´m afraid I don´t know, maybe this is rather well posted at hsm.stackexchange.com
$endgroup$
– Peter Melech
Dec 30 '18 at 15:36
add a comment |
$begingroup$
How does the division method for polynomial discovered. I have read about ruffini method, it needs divisor to be binomial and linear, I tried to understand horner's method, but couldn't. but methods are traditional and different from what I am doing (like this one below):
How this method (image one) came from earlier methods?
polynomials
$endgroup$
How does the division method for polynomial discovered. I have read about ruffini method, it needs divisor to be binomial and linear, I tried to understand horner's method, but couldn't. but methods are traditional and different from what I am doing (like this one below):
How this method (image one) came from earlier methods?
polynomials
polynomials
edited Dec 30 '18 at 14:34
asked Dec 30 '18 at 14:15
user629353
1
$begingroup$
Do You remember the method to divide integers by hand? Polymomial rings have essentially the same structure as the ring of integers.
$endgroup$
– Peter Melech
Dec 30 '18 at 14:24
$begingroup$
Is this fact known in earlier time, then what are horner's and ruffini method
$endgroup$
– user629353
Dec 30 '18 at 14:29
$begingroup$
Did ruffini know that dividing polynomials is similar to how integer division works
$endgroup$
– user629353
Dec 30 '18 at 14:50
$begingroup$
How it came to know that polynomial division is similar to as in integer case
$endgroup$
– user629353
Dec 30 '18 at 14:58
$begingroup$
I´m afraid I don´t know, maybe this is rather well posted at hsm.stackexchange.com
$endgroup$
– Peter Melech
Dec 30 '18 at 15:36
add a comment |
1
$begingroup$
Do You remember the method to divide integers by hand? Polymomial rings have essentially the same structure as the ring of integers.
$endgroup$
– Peter Melech
Dec 30 '18 at 14:24
$begingroup$
Is this fact known in earlier time, then what are horner's and ruffini method
$endgroup$
– user629353
Dec 30 '18 at 14:29
$begingroup$
Did ruffini know that dividing polynomials is similar to how integer division works
$endgroup$
– user629353
Dec 30 '18 at 14:50
$begingroup$
How it came to know that polynomial division is similar to as in integer case
$endgroup$
– user629353
Dec 30 '18 at 14:58
$begingroup$
I´m afraid I don´t know, maybe this is rather well posted at hsm.stackexchange.com
$endgroup$
– Peter Melech
Dec 30 '18 at 15:36
1
1
$begingroup$
Do You remember the method to divide integers by hand? Polymomial rings have essentially the same structure as the ring of integers.
$endgroup$
– Peter Melech
Dec 30 '18 at 14:24
$begingroup$
Do You remember the method to divide integers by hand? Polymomial rings have essentially the same structure as the ring of integers.
$endgroup$
– Peter Melech
Dec 30 '18 at 14:24
$begingroup$
Is this fact known in earlier time, then what are horner's and ruffini method
$endgroup$
– user629353
Dec 30 '18 at 14:29
$begingroup$
Is this fact known in earlier time, then what are horner's and ruffini method
$endgroup$
– user629353
Dec 30 '18 at 14:29
$begingroup$
Did ruffini know that dividing polynomials is similar to how integer division works
$endgroup$
– user629353
Dec 30 '18 at 14:50
$begingroup$
Did ruffini know that dividing polynomials is similar to how integer division works
$endgroup$
– user629353
Dec 30 '18 at 14:50
$begingroup$
How it came to know that polynomial division is similar to as in integer case
$endgroup$
– user629353
Dec 30 '18 at 14:58
$begingroup$
How it came to know that polynomial division is similar to as in integer case
$endgroup$
– user629353
Dec 30 '18 at 14:58
$begingroup$
I´m afraid I don´t know, maybe this is rather well posted at hsm.stackexchange.com
$endgroup$
– Peter Melech
Dec 30 '18 at 15:36
$begingroup$
I´m afraid I don´t know, maybe this is rather well posted at hsm.stackexchange.com
$endgroup$
– Peter Melech
Dec 30 '18 at 15:36
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
I like the following way:
$$2x^3-7x^2+11=2x^3-6x^2-x^2+3x-3x+9+2=(x-3)(2x^2-x-3)+2.$$
answered Dec 30 '18 at 14:29
Michael RozenbergMichael Rozenberg
105k1892198
$endgroup$
$begingroup$
But this splitting may not be sometimes foundable
$endgroup$
– user629353
Dec 30 '18 at 14:31
$begingroup$
@user629353 See please better my solution. We can detect it always. I think, it's much more better than to write that you wrote. Give me another polynomials and I'll make it again.
$endgroup$
– Michael Rozenberg
Dec 30 '18 at 14:33
$begingroup$
Can someone, which down voted my post, explain me your step?
$endgroup$
– Michael Rozenberg
Dec 30 '18 at 14:44
$begingroup$
Yeah, it's better, thanks
$endgroup$
– user629353
Jan 5 at 15:22
$begingroup$
You are welcome!
$endgroup$
– Michael Rozenberg
Jan 5 at 15:25
add a comment |
$begingroup$
So you are asking how the long division that people usually use(i.e. the long division) was derived or infered from the simple ones such as the ruffini method. I'm not sure but you could show that ruffini method is special case of the long division. here is a youtube video showing how they are related for a special case.
answered Dec 30 '18 at 14:38
PyHomerPyHomer
1
$endgroup$
$begingroup$
If synthetic division comes from ruffini method then how did ruffini found it
$endgroup$
– user629353
Dec 30 '18 at 14:42
add a comment |
Your Answer
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I like the following way:
$$2x^3-7x^2+11=2x^3-6x^2-x^2+3x-3x+9+2=(x-3)(2x^2-x-3)+2.$$
answered Dec 30 '18 at 14:29
Michael RozenbergMichael Rozenberg
105k1892198
$endgroup$
$begingroup$
But this splitting may not be sometimes foundable
$endgroup$
– user629353
Dec 30 '18 at 14:31
$begingroup$
@user629353 See please better my solution. We can detect it always. I think, it's much more better than to write that you wrote. Give me another polynomials and I'll make it again.
$endgroup$
– Michael Rozenberg
Dec 30 '18 at 14:33
$begingroup$
Can someone, which down voted my post, explain me your step?
$endgroup$
– Michael Rozenberg
Dec 30 '18 at 14:44
$begingroup$
Yeah, it's better, thanks
$endgroup$
– user629353
Jan 5 at 15:22
$begingroup$
You are welcome!
$endgroup$
– Michael Rozenberg
Jan 5 at 15:25
add a comment |
$begingroup$
I like the following way:
$$2x^3-7x^2+11=2x^3-6x^2-x^2+3x-3x+9+2=(x-3)(2x^2-x-3)+2.$$
answered Dec 30 '18 at 14:29
Michael RozenbergMichael Rozenberg
105k1892198
$endgroup$
$begingroup$
But this splitting may not be sometimes foundable
$endgroup$
– user629353
Dec 30 '18 at 14:31
$begingroup$
@user629353 See please better my solution. We can detect it always. I think, it's much more better than to write that you wrote. Give me another polynomials and I'll make it again.
$endgroup$
– Michael Rozenberg
Dec 30 '18 at 14:33
$begingroup$
Can someone, which down voted my post, explain me your step?
$endgroup$
– Michael Rozenberg
Dec 30 '18 at 14:44
$begingroup$
Yeah, it's better, thanks
$endgroup$
– user629353
Jan 5 at 15:22
$begingroup$
You are welcome!
$endgroup$
– Michael Rozenberg
Jan 5 at 15:25
add a comment |
$begingroup$
I like the following way:
$$2x^3-7x^2+11=2x^3-6x^2-x^2+3x-3x+9+2=(x-3)(2x^2-x-3)+2.$$
answered Dec 30 '18 at 14:29
Michael RozenbergMichael Rozenberg
105k1892198
$endgroup$
I like the following way:
$$2x^3-7x^2+11=2x^3-6x^2-x^2+3x-3x+9+2=(x-3)(2x^2-x-3)+2.$$
answered Dec 30 '18 at 14:29
Michael RozenbergMichael Rozenberg
105k1892198
answered Dec 30 '18 at 14:29
Michael RozenbergMichael Rozenberg
105k1892198
answered Dec 30 '18 at 14:29
Michael RozenbergMichael Rozenberg
105k1892198
answered Dec 30 '18 at 14:29
Michael RozenbergMichael Rozenberg
105k1892198
105k1892198
$begingroup$
But this splitting may not be sometimes foundable
$endgroup$
– user629353
Dec 30 '18 at 14:31
$begingroup$
@user629353 See please better my solution. We can detect it always. I think, it's much more better than to write that you wrote. Give me another polynomials and I'll make it again.
$endgroup$
– Michael Rozenberg
Dec 30 '18 at 14:33
$begingroup$
Can someone, which down voted my post, explain me your step?
$endgroup$
– Michael Rozenberg
Dec 30 '18 at 14:44
$begingroup$
Yeah, it's better, thanks
$endgroup$
– user629353
Jan 5 at 15:22
$begingroup$
You are welcome!
$endgroup$
– Michael Rozenberg
Jan 5 at 15:25
add a comment |
$begingroup$
But this splitting may not be sometimes foundable
$endgroup$
– user629353
Dec 30 '18 at 14:31
$begingroup$
@user629353 See please better my solution. We can detect it always. I think, it's much more better than to write that you wrote. Give me another polynomials and I'll make it again.
$endgroup$
– Michael Rozenberg
Dec 30 '18 at 14:33
$begingroup$
Can someone, which down voted my post, explain me your step?
$endgroup$
– Michael Rozenberg
Dec 30 '18 at 14:44
$begingroup$
Yeah, it's better, thanks
$endgroup$
– user629353
Jan 5 at 15:22
$begingroup$
You are welcome!
$endgroup$
– Michael Rozenberg
Jan 5 at 15:25
$begingroup$
But this splitting may not be sometimes foundable
$endgroup$
– user629353
Dec 30 '18 at 14:31
$begingroup$
But this splitting may not be sometimes foundable
$endgroup$
– user629353
Dec 30 '18 at 14:31
$begingroup$
@user629353 See please better my solution. We can detect it always. I think, it's much more better than to write that you wrote. Give me another polynomials and I'll make it again.
$endgroup$
– Michael Rozenberg
Dec 30 '18 at 14:33
$begingroup$
@user629353 See please better my solution. We can detect it always. I think, it's much more better than to write that you wrote. Give me another polynomials and I'll make it again.
$endgroup$
– Michael Rozenberg
Dec 30 '18 at 14:33
$begingroup$
Can someone, which down voted my post, explain me your step?
$endgroup$
– Michael Rozenberg
Dec 30 '18 at 14:44
$begingroup$
Can someone, which down voted my post, explain me your step?
$endgroup$
– Michael Rozenberg
Dec 30 '18 at 14:44
$begingroup$
Yeah, it's better, thanks
$endgroup$
– user629353
Jan 5 at 15:22
$begingroup$
Yeah, it's better, thanks
$endgroup$
– user629353
Jan 5 at 15:22
$begingroup$
You are welcome!
$endgroup$
– Michael Rozenberg
Jan 5 at 15:25
$begingroup$
You are welcome!
$endgroup$
– Michael Rozenberg
Jan 5 at 15:25
add a comment |
$begingroup$
So you are asking how the long division that people usually use(i.e. the long division) was derived or infered from the simple ones such as the ruffini method. I'm not sure but you could show that ruffini method is special case of the long division. here is a youtube video showing how they are related for a special case.
answered Dec 30 '18 at 14:38
PyHomerPyHomer
1
$endgroup$
$begingroup$
If synthetic division comes from ruffini method then how did ruffini found it
$endgroup$
– user629353
Dec 30 '18 at 14:42
add a comment |
$begingroup$
So you are asking how the long division that people usually use(i.e. the long division) was derived or infered from the simple ones such as the ruffini method. I'm not sure but you could show that ruffini method is special case of the long division. here is a youtube video showing how they are related for a special case.
answered Dec 30 '18 at 14:38
PyHomerPyHomer
1
$endgroup$
$begingroup$
If synthetic division comes from ruffini method then how did ruffini found it
$endgroup$
– user629353
Dec 30 '18 at 14:42
add a comment |
$begingroup$
So you are asking how the long division that people usually use(i.e. the long division) was derived or infered from the simple ones such as the ruffini method. I'm not sure but you could show that ruffini method is special case of the long division. here is a youtube video showing how they are related for a special case.
answered Dec 30 '18 at 14:38
PyHomerPyHomer
1
$endgroup$
So you are asking how the long division that people usually use(i.e. the long division) was derived or infered from the simple ones such as the ruffini method. I'm not sure but you could show that ruffini method is special case of the long division. here is a youtube video showing how they are related for a special case.
answered Dec 30 '18 at 14:38
PyHomerPyHomer
1
answered Dec 30 '18 at 14:38
PyHomerPyHomer
1
answered Dec 30 '18 at 14:38
PyHomerPyHomer
1
answered Dec 30 '18 at 14:38
PyHomerPyHomer
1
1
$begingroup$
If synthetic division comes from ruffini method then how did ruffini found it
$endgroup$
– user629353
Dec 30 '18 at 14:42
add a comment |
$begingroup$
If synthetic division comes from ruffini method then how did ruffini found it
$endgroup$
– user629353
Dec 30 '18 at 14:42
$begingroup$
If synthetic division comes from ruffini method then how did ruffini found it
$endgroup$
– user629353
Dec 30 '18 at 14:42
$begingroup$
If synthetic division comes from ruffini method then how did ruffini found it
$endgroup$
– user629353
Dec 30 '18 at 14:42
add a comment |
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1
$begingroup$
Do You remember the method to divide integers by hand? Polymomial rings have essentially the same structure as the ring of integers.
$endgroup$
– Peter Melech
Dec 30 '18 at 14:24
$begingroup$
Is this fact known in earlier time, then what are horner's and ruffini method
$endgroup$
– user629353
Dec 30 '18 at 14:29
$begingroup$
Did ruffini know that dividing polynomials is similar to how integer division works
$endgroup$
– user629353
Dec 30 '18 at 14:50
$begingroup$
How it came to know that polynomial division is similar to as in integer case
$endgroup$
– user629353
Dec 30 '18 at 14:58
$begingroup$
I´m afraid I don´t know, maybe this is rather well posted at hsm.stackexchange.com
$endgroup$
– Peter Melech
Dec 30 '18 at 15:36