Polynomial in ascending power of x

Alex shared this question 2 years ago

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I have a polynomial, say a random polynomial of degree 3. Is there a way to turn it into another equivalent polynomial in ascending powers of x?

Thanks.

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Best Answer

Jozef Dobos ● 2 years ago

see attached file

Files: aha_algebra.ggb

Comments (16)

Noel Lambert ● 2 years ago

with text ? (no other polynomial)

Files: croissant.ggb

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Alex ● 2 years ago

Thanks for your help.

But when some of the coefficients are zero or one, your expression is not good enough for me.

When f(x)=x^3-x+4, I need another polynomial g(x)=4-x+x^3. Nothing more, nothing less.

Many thanks,

Alex

Files: Screenshot 2020...

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Jozef Dobos ● 2 years ago

see attached file

Files: aha.ggb

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Alex ● 2 years ago

Sorry your method seems work only in CAS environment. In normal Graphic View, the zeros and ones still appear. I try to avoid CAS methods like Simplify, Expand, etc.

See attached file.

Thanks anyway.

Files: aha2.ggb

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mathmagic ● 2 years ago

is TaylorPolynomial(f, 0, Degree(f)) enough?

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Alex ● 2 years ago

Not exactly. Thanks.

Files: Screenshot 2020...

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mathmagic ● 2 years ago

más detalles corren por cuenta del proximo autor

Files: foro.ggb

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Elżbieta Kotlicka-Dwurznik ● 2 years ago

Maybe something like that

/BwcHBodr4fzvktkjwXSh4AAAAAElFTkSuQmCC

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Jozef Dobos ● 2 years ago ●

see attached file

Files: aha_algebra.ggb

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Alex ● 2 years ago

Thanks. But Simplify() invokes CAS, which is not preferred.

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mathmagic ● 2 years ago

me gusta este ultimo

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Elżbieta Kotlicka-Dwurznik ● 2 years ago

Correction of my answer: r(x)=a+Polynomial(b*x)+Polynomial(c*x^2)+Polynomial(d*x^3)

but I agree that Jozef's answer is better :)

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Alex ● 2 years ago

Thanks. This is nearly perfect, except when a=b=0 and c=5, it gives result 0+5x^2 instead of 5x^2.

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jumera ● 2 years ago

So...

Files: ahaha_algebra.g...

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Alex ● 2 years ago

Thanks! https://www.geogebra.org/m/u2hgmccf

Hope other users can benefit.

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Elżbieta Kotlicka-Dwurznik ● 2 years ago

or If(a^2+b^2==0,Polynomial(c x^2),r(x))

but it works only for quadratic function

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